Completing Statements MCQs for Sub-Topics of Topic 7: Mensuration

Question 1. Mensuration is the branch of mathematics that deals with the measurement of_____

(A) angles and lines only.

(B) shapes and positions only.

(C) length, area, and volume of geometric figures.

(D) symmetry and transformations.

Question 2. The total length of the boundary of a closed plane figure is known as its_____

(A) area.

(B) volume.

(C) surface area.

(D) perimeter.

Question 3. The amount of surface enclosed by a closed plane figure is called its_____

(A) perimeter.

(B) volume.

(C) area.

(D) circumference.

Question 4. Perimeter is a measurement of length, and its standard units include_____

(A) square metres ($\text{m}^2$).

(B) cubic centimetres ($\text{cm}^3$).

(C) metres ($\text{m}$).

(D) hectares ($\text{ha}$).

Question 5. Area is a measurement of surface, and its standard units include_____

(A) centimetres ($\text{cm}$).

(B) square kilometres ($\text{km}^2$).

(C) litres ($\text{L}$).

(D) metres ($\text{m}$).

Question 6. A closed plane figure is required to have a well-defined_____

(A) volume.

(B) surface area.

(C) perimeter and area.

(D) height and width.

Question 7. The concept of volume in mensuration deals with the measurement of_____

(A) the outer boundary of a 3D shape.

(B) the flat surfaces of a 3D shape.

(C) the space occupied by a 3D solid.

(D) the length of edges of a 3D shape.

Question 8. Converting $10\ \text{metres}$ to centimetres involves multiplying by_____

(A) 10.

(B) 100.

(C) 1000.

(D) 0.01.

Question 9. Converting $1\ \text{square kilometre}$ to square metres involves multiplying by_____

(A) 1000.

(B) 10000.

(C) 100000.

(D) 1000000.

Question 10. A field measuring $1\ \text{hectare}$ has an area equivalent to_____

(A) $100\ \text{m}^2$.

(B) $1000\ \text{m}^2$.

(C) $10000\ \text{m}^2$.

(D) $100000\ \text{m}^2$.

Question 1. The perimeter of any polygon is found by_____

(A) multiplying the number of sides by the average side length.

(B) summing the lengths of all its sides.

(C) multiplying the length of the longest side by the number of vertices.

(D) finding the product of its longest and shortest sides.

Question 2. The formula for the perimeter of a square with side length $s$ is_____

(A) $s^2$.

(B) $2s$.

(C) $4s$.

(D) $s/4$.

Question 3. The perimeter of a rectangle with length $l$ and width $w$ can be calculated as_____

(A) $l \times w$.

(B) $l + w$.

(C) $2(l+w)$.

(D) $l^2 + w^2$.

Question 4. For a triangle with side lengths $a, b, c$, its perimeter is given by_____

(A) $a \times b \times c$.

(B) $\frac{1}{2}(a+b+c)$.

(C) $a+b+c$.

(D) $\sqrt{a+b+c}$.

Question 5. The perimeter of a parallelogram with adjacent sides of length $x$ and $y$ is_____

(A) $x+y$.

(B) $xy$.

(C) $2(x+y)$.

(D) $\sqrt{x^2+y^2}$.

Question 6. If a regular hexagon has a side length of $p$, its perimeter is_____

(A) $p^2$.

(B) $6p$.

(C) $p/6$.

(D) $\sqrt{p}$.

Question 7. A wire of length $W$ is used to form the boundary of a rectangular field. The perimeter of the field will be equal to_____

(A) the area of the field.

(B) the length of the wire, $W$.

(C) half the length of the wire.

(D) the square of the length of the wire.

Question 8. If the perimeter of a square field is $100\ \text{m}$, the length of each side is_____

(A) $10\ \text{m}$.

(B) $25\ \text{m}$.

(C) $50\ \text{m}$.

(D) $100\ \text{m}$.

Question 9. An isosceles triangle has two equal sides. If the perimeter is $P$ and the unequal side is $u$, the length of each equal side is_____

(A) $P-u$.

(B) $\frac{P-u}{2}$.

(C) $P-2u$.

(D) $\frac{P+u}{2}$.

Question 10. The perimeter of a rhombus with side length $z$ is given by_____

(A) $z^2$.

(B) $2z$.

(C) $4z$.

(D) $z/4$.

Question 1. The area of a square with side length $s$ is calculated as_____

(A) $2s$.

(B) $4s$.

(C) $s^2$.

(D) $s/2$.

Question 2. For a rectangle with length $l$ and width $w$, its area is given by the formula_____

(A) $2(l+w)$.

(B) $l \times w$.

(C) $l+w$.

(D) $l^2 + w^2$.

Question 3. The area of a triangle with base $b$ and corresponding height $h$ is calculated using the formula_____

(A) $b \times h$.

(B) $2 \times b \times h$.

(C) $\frac{1}{2} \times b \times h$.

(D) $\sqrt{b \times h}$.

Question 4. The area of a parallelogram with base $B$ and corresponding height $H$ is_____

(A) $B+H$.

(B) $2(B+H)$.

(C) $\frac{1}{2}BH$.

(D) $BH$.

Question 5. If the area of a square is $144\ \text{cm}^2$, the length of its side is_____

(A) $12\ \text{cm}$.

(B) $14.4\ \text{cm}$.

(C) $36\ \text{cm}$.

(D) $72\ \text{cm}$.

Question 6. A rectangular room is $8\ \text{m}$ long and $6\ \text{m}$ wide. The area of the floor is_____

(A) $14\ \text{m}^2$.

(B) $28\ \text{m}^2$.

(C) $48\ \text{m}^2$.

(D) $24\ \text{m}^2$.

Question 7. If the area of a rectangle is $A$ and its length is $l$, its width $w$ can be found by_____

(A) $w = A \times l$.

(B) $w = A/l$.

(C) $w = A-l$.

(D) $w = l/A$.

Question 8. A triangle and a parallelogram have the same base and are between the same parallel lines. The area of the triangle is_____

(A) equal to the area of the parallelogram.

(B) twice the area of the parallelogram.

(C) half the area of the parallelogram.

(D) one-third the area of the parallelogram.

Question 9. The area of a trapezium with parallel sides $a$ and $b$ and height $h$ is_____

(A) $(a+b)h$.

(B) $ab h$.

(C) $\frac{1}{2}(a+b)h$.

(D) $\frac{1}{2}ab h$.

Question 10. If the base of a triangle is $15\ \text{cm}$ and its area is $60\ \text{cm}^2$, its corresponding height is_____

(A) $4\ \text{cm}$.

(B) $8\ \text{cm}$.

(C) $12\ \text{cm}$.

(D) $15\ \text{cm}$.

Question 1. Heron's formula is used to find the area of a triangle when_____

(A) the base and height are known.

(B) it is a right-angled triangle.

(C) the lengths of all three sides are known.

(D) it is an equilateral triangle.

Question 2. For a triangle with sides $a, b, c$, the semi-perimeter $s$ is defined as_____

(A) $a+b+c$.

(B) $2(a+b+c)$.

(C) $\frac{a+b+c}{2}$.

(D) $\sqrt{a+b+c}$.

Question 3. Heron's formula for the area of a triangle with sides $a, b, c$ and semi-perimeter $s$ is_____

(A) $s(s-a)(s-b)(s-c)$.

(B) $\sqrt{(s-a)(s-b)(s-c)}$.

(C) $\sqrt{s(s-a)(s-b)(s-c)}$.

(D) $s^2 (s-a)(s-b)(s-c)$.

Question 4. For an equilateral triangle with side length $a$, the semi-perimeter is_____

(A) $a/2$.

(B) $3a$.

(C) $3a/2$.

(D) $a^2$.

Question 5. Using Heron's formula, the area of an equilateral triangle with side $a$ simplifies to_____

(A) $a^2$.

(B) $\frac{1}{2}a^2$.

(C) $\frac{\sqrt{3}}{4}a^2$.

(D) $\sqrt{3}a^2$.

Question 6. An isosceles triangle has equal sides of length $x$ and a base of length $y$. The semi-perimeter is_____

(A) $x+y$.

(B) $2x+y$.

(C) $x + y/2$.

(D) $2(x+y)$.

Question 7. The perimeter of a triangle is $P$. If the side lengths are $a, b, c$, then $P$ is equal to_____

(A) $2s$.

(B) $s/2$.

(C) $s$.

(D) $s^2$.

Question 8. If for a triangle with sides $a, b, c$, the expression $s(s-a)(s-b)(s-c)$ under the square root is zero, it means the triangle is_____

(A) equilateral.

(B) right-angled.

(C) degenerate (the vertices are collinear).

(D) isosceles.

Question 9. Given the sides of a triangle as $9\ \text{cm}$, $12\ \text{cm}$, and $15\ \text{cm}$, its semi-perimeter is_____

(A) $18\ \text{cm}$.

(B) $36\ \text{cm}$.

(C) $12\ \text{cm}$.

(D) $15\ \text{cm}$.

Question 10. For the triangle with sides $9\ \text{cm}$, $12\ \text{cm}$, $15\ \text{cm}$, its area using Heron's formula is $\sqrt{18(18-9)(18-12)(18-15)} = \sqrt{18 \times 9 \times 6 \times 3} = \sqrt{2916}$, which equals_____

(A) $54\ \text{cm}^2$.

(B) $72\ \text{cm}^2$.

(C) $81\ \text{cm}^2$.

(D) $90\ \text{cm}^2$.

Question 1. The area of a rhombus with diagonals $d_1$ and $d_2$ is given by the formula_____

(A) $d_1 d_2$.

(B) $2 d_1 d_2$.

(C) $\frac{1}{2} d_1 d_2$.

(D) $\sqrt{d_1^2+d_2^2}$.

Question 2. For a general quadrilateral with a diagonal $d$, and perpendiculars $h_1$ and $h_2$ drawn from the opposite vertices to this diagonal, the area is_____

(A) $d(h_1+h_2)$.

(B) $\frac{1}{2}d(h_1+h_2)$.

(C) $d h_1 h_2$.

(D) $\sqrt{d h_1 h_2}$.

Question 3. To find the area of a quadrilateral by dividing it into two triangles using a diagonal, you would_____

(A) calculate the area of the quadrilateral directly using its four sides.

(B) sum the areas of the two triangles formed by the diagonal.

(C) multiply the area of one triangle by two.

(D) use a specific formula for that type of quadrilateral only.

Question 4. The area of a kite with diagonals $D_1$ and $D_2$ is calculated using the formula_____

(A) $D_1 + D_2$.

(B) $\frac{1}{2}(D_1+D_2)$.

(C) $D_1 D_2$.

(D) $\frac{1}{2} D_1 D_2$.

Question 5. A rhombus has diagonals of length $10\ \text{cm}$ and $24\ \text{cm}$. Its area is_____

(A) $60\ \text{cm}^2$.

(B) $120\ \text{cm}^2$.

(C) $240\ \text{cm}^2$.

(D) $13\ \text{cm}^2$.

Question 6. To find the area of a general polygon with $n$ sides, a common method is to divide it into non-overlapping_____

(A) rectangles.

(B) squares.

(C) circles.

(D) triangles.

Question 7. If the diagonals of a parallelogram are perpendicular, the parallelogram is a_____

(A) rectangle.

(B) square.

(C) rhombus.

(D) trapezium.

Question 8. A general quadrilateral ABCD has diagonal AC = $18\ \text{cm}$, and perpendiculars from B and D to AC are $5\ \text{cm}$ and $7\ \text{cm}$ respectively. The area of the quadrilateral is_____

(A) $18(5+7) = 216\ \text{cm}^2$.

(B) $\frac{1}{2} \times 18 \times (5+7) = 9 \times 12 = 108\ \text{cm}^2$.

(C) $\frac{1}{2} \times 18 \times 5 + \frac{1}{2} \times 18 \times 7 = 45 + 63 = 108\ \text{cm}^2$.

(D) Both (B) and (C) are correct.

Question 9. The area of a regular $n$-sided polygon with side length $s$ and apothem $a$ is given by_____

(A) $ns \times a$.

(B) $\frac{1}{2} \times (ns) \times a$.

(C) $\sqrt{(ns) \times a}$.

(D) $n \times s \times a$.

Question 10. A kite has diagonals measuring $14\ \text{m}$ and $10\ \text{m}$. The area of the kite is_____

(A) $24\ \text{m}^2$.

(B) $70\ \text{m}^2$.

(C) $140\ \text{m}^2$.

(D) $280\ \text{m}^2$.

Question 1. The circumference of a circle is also known as its_____

(A) area.

(B) radius.

(C) diameter.

(D) perimeter.

Question 2. The formula for the circumference of a circle with radius $r$ is_____

(A) $\pi r^2$.

(B) $2\pi r$.

(C) $\frac{1}{2}\pi r^2$.

(D) $\pi r$.

Question 3. The area of a circle with radius $r$ is given by the formula_____

(A) $2\pi r$.

(B) $\pi r^2$.

(C) $\frac{1}{2}\pi r^2$.

(D) $\pi d$ (where $d$ is diameter).

Question 4. If the diameter of a circle is $10\ \text{cm}$, its radius is_____

(A) $5\ \text{cm}$.

(B) $10\ \text{cm}$.

(C) $20\ \text{cm}$.

(D) $100\ \text{cm}$.

Question 5. Using $\pi = \frac{22}{7}$, the circumference of a circle with radius $7\ \text{cm}$ is_____

(A) $22\ \text{cm}$.

(B) $44\ \text{cm}$.

(C) $88\ \text{cm}$.

(D) $154\ \text{cm}$.

Question 6. Using $\pi = \frac{22}{7}$, the area of a circle with radius $14\ \text{cm}$ is_____

(A) $44\ \text{cm}^2$.

(B) $88\ \text{cm}^2$.

(C) $154\ \text{cm}^2$.

(D) $616\ \text{cm}^2$.

Question 7. If the circumference of a circle is $C$ and its radius is $r$, the relationship between area ($A$) and circumference is $A = \frac{C \times r}{2}$, because_____

(A) $C=2\pi r$ and $A=\pi r^2$, so $A = \pi r^2 = \frac{(2\pi r)r}{2} = \frac{Cr}{2}$.

(B) $A = C/r$.

(C) $A = C^2$.

(D) $A = C+r$.

Question 8. If the radius of a circle is halved, its circumference becomes_____

(A) doubled.

(B) halved.

(C) four times.

(D) one-fourth.

Question 9. If the radius of a circle is halved, its area becomes_____

(A) doubled.

(B) halved.

(C) four times.

(D) one-fourth.

Question 10. The ratio of the circumference of a circle to its diameter is a constant value denoted by_____

(A) 2.

(B) $\pi$.

(C) $2\pi$.

(D) $\pi^2$.

Question 1. A sector of a circle is the region enclosed by two radii and an_____

(A) chord.

(B) tangent.

(C) arc.

(D) diameter.

Question 2. The length of an arc of a sector with radius $r$ and central angle $\theta$ (in degrees) is given by_____

(A) $\frac{\theta}{360} \times \pi r^2$.

(B) $\frac{\theta}{360} \times 2\pi r$.

(C) $\frac{\theta}{180} \times \pi r$.

(D) $r\theta$ (assuming $\theta$ in radians).

Question 3. The area of a sector of a circle with radius $r$ and central angle $\theta$ (in degrees) is calculated as_____

(A) $\frac{\theta}{360} \times 2\pi r$.

(B) $\frac{\theta}{360} \times \pi r^2$.

(C) $\frac{1}{2} \times \text{arc length} \times \text{diameter}$.

(D) $\pi r^2 \times \theta$.

Question 4. A segment of a circle is the region bounded by a chord and an_____

(A) radius.

(B) diameter.

(C) tangent.

(D) arc.

Question 5. The area of a minor segment of a circle is found by subtracting the area of the triangle formed by the radii and the chord from the area of the corresponding_____

(A) circle.

(B) major segment.

(C) sector.

(D) semicircle.

Question 6. A sector with a central angle of $180^\circ$ is also known as a_____

(A) quadrant.

(B) semicircle.

(C) segment.

(D) diameter.

Question 7. If a sector has radius $r$ and arc length $l$, its area can also be given by the formula_____

(A) $rl$.

(B) $\frac{1}{2}rl$.

(C) $\pi r l$.

(D) $2rl$.

Question 8. The perimeter of a sector with radius $r$ and arc length $l$ is the sum of $2r$ and_____

(A) $\pi r^2$.

(B) $\theta$ (central angle).

(C) $l$.

(D) area of the sector.

Question 9. If a chord of a circle is equal to its radius, the triangle formed by the two radii and the chord is an_____

(A) isosceles triangle.

(B) equilateral triangle.

(C) right-angled triangle.

(D) obtuse-angled triangle.

Question 10. The area of the major segment of a circle is equal to the area of the circle minus the area of the_____

(A) corresponding sector.

(B) corresponding triangle.

(C) minor segment.

(D) major sector.

Question 1. To find the area of a region formed by combining several basic plane figures without overlap, you would_____

(A) multiply their areas.

(B) subtract the smallest area from the largest area.

(C) sum the areas of the individual figures.

(D) find the average of their areas.

Question 2. When a smaller plane figure is removed from a larger plane figure, the area of the remaining portion is found by_____

(A) adding the areas of the two figures.

(B) subtracting the area of the smaller figure from the area of the larger figure.

(C) multiplying their areas.

(D) finding the difference between their perimeters.

Question 3. The perimeter of a composite plane figure is the total length of its_____

(A) internal boundaries.

(B) outer boundary.

(C) sum of all boundary lines (internal and external).

(D) sum of the perimeters of the individual figures.

Question 4. A path of uniform width runs outside a rectangular park. The area of the path is calculated as the area of the outer rectangle minus the area of the inner rectangle, where the inner rectangle is the_____

(A) path itself.

(B) original park.

(C) area covered by the path.

(D) area around the path.

Question 5. A path of uniform width runs inside a square park. The area of the path is calculated as the area of the outer square (park boundary) minus the area of the inner square, where the inner square is the_____

(A) path itself.

(B) region inside the path.

(C) area covered by the path.

(D) area around the path.

Question 6. If a semicircle is attached to one side of a square, the perimeter of the resulting composite figure includes the lengths of the three sides of the square plus the length of the_____

(A) diameter of the semicircle.

(B) radius of the semicircle.

(C) arc of the semicircle.

(D) area of the semicircle.

Question 7. Two circular parks are concentric. A path is built in the region between them. The area of this circular path (ring) is the area of the outer circle minus the area of the_____

(A) path width.

(B) circumference.

(C) inner circle.

(D) radius difference.

Question 8. If a rectangular piece has identical semicircles attached to both of its shorter sides as diameters, the area of the combined shape is the area of the rectangle plus the area of_____

(A) one semicircle.

(B) one circle (formed by the two semicircles).

(C) two circles (one for each semicircle).

(D) the region between the rectangle and the semicircles.

Question 9. When solving problems involving areas and perimeters of combined figures, it is important to correctly identify the boundaries that contribute to the perimeter and the non-overlapping regions that contribute to the_____

(A) volume.

(B) surface area.

(C) area.

(D) length.

Question 10. A design consists of a square with four identical quadrants of a circle at its corners. To find the area of the region inside the square but outside the quadrants, you would subtract the total area of the four quadrants from the area of the_____

(A) one quadrant.

(B) circle from which the quadrants were cut.

(C) square.

(D) region between the quadrants.

Question 1. Solid shapes are figures that have three dimensions: length, width, and_____

(A) area.

(B) volume.

(C) depth or height.

(D) perimeter.

Question 2. The flat or curved surfaces that make up the boundary of a solid figure are called its_____

(A) edges.

(B) vertices.

(C) faces.

(D) bases.

Question 3. The line segments where two faces of a solid figure meet are called its_____

(A) vertices.

(B) edges.

(C) corners.

(D) lines.

Question 4. The points where three or more edges meet in a solid figure are called its_____

(A) faces.

(B) edges.

(C) vertices.

(D) sides.

Question 5. A cube is a solid figure with 6 equal square_____

(A) edges.

(B) vertices.

(C) faces.

(D) diagonals.

Question 6. A solid shape with a circular base and a curved surface tapering to a point (apex) is called a_____

(A) cylinder.

(B) sphere.

(C) cone.

(D) pyramid.

Question 7. A solid shape with two parallel and congruent circular bases joined by a curved surface is called a_____

(A) cone.

(B) cylinder.

(C) sphere.

(D) prism.

Question 8. A solid shape that is perfectly round, where every point on its surface is equidistant from its center, is called a_____

(A) circle.

(B) hemisphere.

(C) cylinder.

(D) sphere.

Question 9. A polyhedron is a solid figure whose faces are_____

(A) curved surfaces.

(B) circles.

(C) polygons.

(D) sectors.

Question 10. According to Euler's formula for polyhedrons, the relationship between the number of faces (F), vertices (V), and edges (E) is_____

(A) $F + V = E$.

(B) $F + E = V + 2$.

(C) $V + E = F + 2$.

(D) $F + V - E = 2$.

Question 1. The surface area of a solid is the sum of the areas of all its_____

(A) edges.

(B) vertices.

(C) faces (and curved surfaces).

(D) volume.

Question 2. The area of the side faces of a prism or pyramid, excluding the base(s), is called the_____

(A) Total Surface Area (TSA).

(B) Lateral Surface Area (LSA).

(C) Curved Surface Area (CSA).

(D) Base Area.

Question 3. For a cuboid with length $l$, width $w$, and height $h$, the Total Surface Area (TSA) is_____

(A) $lwh$.

(B) $2(lw+wh+hl)$.

(C) $l+w+h$.

(D) $lw+wh+hl$.

Question 4. The Lateral Surface Area (LSA) of a cube with side length $a$ is_____

(A) $a^2$.

(B) $6a^2$.

(C) $4a^2$.

(D) $a^3$.

Question 5. The Curved Surface Area (CSA) of a cylinder with radius $r$ and height $h$ is_____

(A) $\pi r^2 h$.

(B) $2\pi r h$.

(C) $\pi r^2$.

(D) $2\pi r^2 + 2\pi r h$.

Question 6. For a solid cylinder with radius $r$ and height $h$, the Total Surface Area (TSA) is_____

(A) $2\pi r h$.

(B) $\pi r^2 h$.

(C) $2\pi r^2$.

(D) $2\pi r (r+h)$.

Question 7. The Curved Surface Area (CSA) of a cone with radius $r$ and slant height $l$ is_____

(A) $\pi r^2$.

(B) $2\pi r$.

(C) $\pi r l$.

(D) $\frac{1}{3}\pi r^2 h$ (where $h$ is height).

Question 8. The surface area of a sphere with radius $r$ is given by the formula_____

(A) $\frac{4}{3}\pi r^3$.

(B) $2\pi r^2$.

(C) $4\pi r^2$.

(D) $\pi r^2 h$ (where $h$ is height).

Question 9. The Curved Surface Area (CSA) of a hemisphere with radius $r$ is_____

(A) $\pi r^2$.

(B) $2\pi r^2$.

(C) $3\pi r^2$.

(D) $4\pi r^2$.

Question 10. For a solid hemisphere with radius $r$, the Total Surface Area (TSA) is the sum of the curved surface area and the area of the base, which is_____

(A) $2\pi r^2 + \pi r^2 = 3\pi r^2$.

(B) $2\pi r^2$.

(C) $3\pi r^2 + \pi r^2 = 4\pi r^2$.

(D) $3\pi r^2 + 2\pi r^2 = 5\pi r^2$.

Question 1. Volume is the measure of the space occupied by a solid and is measured in_____

(A) square units.

(B) linear units.

(C) cubic units.

(D) area units.

Question 2. The formula for the volume of a cube with side length $a$ is_____

(A) $a^2$.

(B) $4a$.

(C) $6a^2$.

(D) $a^3$.

Question 3. The volume of a cuboid with length $l$, width $w$, and height $h$ is given by_____

(A) $2(l+w+h)$.

(B) $l+w+h$.

(C) $lwh$.

(D) $lw+wh+hl$.

Question 4. For a cylinder with base radius $r$ and height $h$, its volume is calculated using the formula_____

(A) $2\pi r h$.

(B) $\pi r^2 h$.

(C) $2\pi r (r+h)$.

(D) $\frac{1}{3}\pi r^2 h$.

Question 5. The volume of a cone with base radius $r$ and height $h$ is one-third the volume of a cylinder with the same base and height, and the formula is_____

(A) $\pi r^2 h$.

(B) $\frac{1}{3}\pi r^2 h$.

(C) $2\pi r h$.

(D) $\pi r^2$.

Question 6. The volume of a sphere with radius $r$ is given by the formula_____

(A) $4\pi r^2$.

(B) $\pi r^2 h$.

(C) $\frac{4}{3}\pi r^3$.

(D) $\frac{2}{3}\pi r^3$.

Question 7. For a hemisphere with radius $r$, its volume is half the volume of a sphere with the same radius, and the formula is_____

(A) $\frac{4}{3}\pi r^3$.

(B) $\frac{2}{3}\pi r^3$.

(C) $2\pi r^2$.

(D) $3\pi r^2$.

Question 8. If the side length of a cube is doubled, its volume becomes_____

(A) doubled.

(B) four times.

(C) six times.

(D) eight times.

Question 9. The capacity of a container is a measure of the volume of substance it can hold and is often expressed in units like litres or_____

(A) square metres ($\text{m}^2$).

(B) cubic metres ($\text{m}^3$).

(C) metres ($\text{m}$).

(D) hectares ($\text{ha}$).

Question 10. The volume of any prism is equal to the area of its base multiplied by its_____

(A) perimeter.

(B) lateral surface area.

(C) slant height.

(D) height.

Question 1. When two basic solids are joined together to form a new solid, the volume of the new solid is the sum of the volumes of the individual solids, assuming they do not_____

(A) have curved surfaces.

(B) have flat bases.

(C) overlap.

(D) have the same radius.

Question 2. To calculate the total surface area of a solid formed by joining two solids, you must consider the areas of all the surfaces that are exposed to the_____ (A) joint. (B) inside. (C) outside. (D) base.

Question 3. A cylindrical container has a hemispherical bottom. Which statement about its total volume is NOT correct? (A) Volume = Volume of cylinder + Volume of hemisphere. (B) If the radius is $r$ and cylinder height is $h$, Volume = $\pi r^2 h + \frac{2}{3}\pi r^3$. (C) Volume = $\pi r^2 (h + \frac{2}{3}r)$. (D) Volume = Area of cylinder base $\times$ total height.

Question 4. A solid is formed by scooping out a cone from a cylinder of the same base and height. Which statement about the volume of the remaining solid is NOT correct? (A) Volume of remaining solid = Volume of cylinder $-$ Volume of cone. (B) If cylinder volume is $V_{cyl}$, the volume of the remaining solid is $\frac{2}{3} V_{cyl}$. (C) The volume of the removed cone is $\frac{1}{3}$ the volume of the cylinder. (D) Volume of remaining solid = Area of base $\times$ height.

Question 5. When a solid is formed by placing one object on top of another, the area of the common boundary surface is not exposed to the outside. Which statement about calculating the total surface area is NOT correct? (A) Sum the total surface areas of the individual objects and subtract the area of the common boundary twice. (B) Sum the exposed surface areas of the individual objects. (C) Sum the curved surface areas and the areas of any exposed flat bases/tops. (D) The TSA is simply the sum of the CSAs of the objects.

Question 6. A decorative block is made by placing a hemisphere on the top of a cube. The base of the hemisphere is equal to the top face of the cube. If the side of the cube is $a$, which statement is NOT correct about the total surface area? (A) Area of base of cube $= a^2$. (B) Area of 4 side faces of cube $= 4a^2$. (C) Curved surface area of hemisphere $= 2\pi (a/2)^2 = \pi a^2/2$. (D) Total Surface Area = Area of 6 faces of cube + CSA of hemisphere.

Question 7. A solid is composed of a cylinder with hemispherical ends. The radius of the hemisphere is equal to the radius of the cylinder. Which statement about the total volume is NOT correct? (A) Volume = Volume of cylinder + 2 $\times$ Volume of hemisphere. (B) If radius is $r$ and cylinder height is $h$, Volume = $\pi r^2 h + 2 \times \frac{2}{3}\pi r^3 = \pi r^2 h + \frac{4}{3}\pi r^3$. (C) Volume = $\pi r^2 (h + \frac{4}{3}r)$. (D) Volume is proportional to the total height of the solid.

Question 8. When a solid object is immersed in a liquid, the volume of the displaced liquid is equal to the volume of the submerged part of the object. Which situation does NOT demonstrate this principle directly? (A) Measuring the volume of an irregular stone by water displacement. (B) A boat floating on water. (C) A solid cylinder fully submerged in a measuring cylinder. (D) Calculating the weight of an object from its density and volume.

Question 9. A hollow cylinder is open at both ends. Which statement is NOT correct about calculating the surface area of the hollow cylinder? (A) It has an inner curved surface area and an outer curved surface area. (B) It has a top annular (ring) area and a bottom annular area. (C) The total surface area is the sum of inner CSA, outer CSA, top ring area, and bottom ring area. (D) The total surface area is $2\pi R h + 2\pi r h + 2\pi (R^2 - r^2)$.

Question 10. A toy is in the shape of a cone on a hemisphere. The radius of the hemisphere is $3\ \text{cm}$ and the height of the cone is $4\ \text{cm}$. Which statement is NOT correct about the total surface area of the toy? (A) The slant height of the cone is $\sqrt{3^2+4^2} = 5\ \text{cm}$. (B) CSA of cone = $\pi (3)(5) = 15\pi\ \text{cm}^2$. (C) CSA of hemisphere $= 2\pi (3)^2 = 18\pi\ \text{cm}^2$. (D) Total Surface Area = CSA of cone $+$ CSA of hemisphere $+$ Area of cone base.

Question 1. When a solid is melted and recast into another shape, the property that remains conserved is its_____

(A) surface area.

(B) volume.

(C) height.

(D) radius.

Question 2. If earth is dug out from a cylindrical well and spread evenly to form a rectangular platform, the volume of earth dug out is equal to the volume of the_____

(A) well.

(B) platform.

(C) well's surface area.

(D) well's perimeter.

Question 3. A frustum of a cone is formed when a cone is cut by a plane parallel to its base, and the part remaining between the plane and the base is kept. A frustum therefore has two circular bases that are parallel and_____

(A) congruent.

(B) perpendicular.

(C) of different radii.

(D) intersecting.

Question 4. The formula for the volume of a frustum of a cone with height $h$ and radii $r_1$ and $r_2$ is $\frac{1}{3}\pi h (_____)$

(A) $(r_1 + r_2)$.

(B) $(r_1^2 + r_2^2)$.

(C) $(r_1 + r_2)^2$.

(D) $(r_1^2 + r_2^2 + r_1 r_2)$.

Question 5. The curved surface area (CSA) of a frustum of a cone with slant height $l$ and radii $r_1$ and $r_2$ is given by the formula $\pi l (_____)$

(A) $(r_1 + r_2)$.

(B) $(r_1 - r_2)$.

(C) $(r_1^2 + r_2^2)$.

(D) $r_1 r_2$.

Question 6. The slant height $l$ of a frustum of a cone with height $h$ and radii $r_1$ and $r_2$ is calculated using the formula $l = \sqrt{h^2 + (_____)}$.

(A) $r_1^2$.

(B) $r_2^2$.

(C) $(r_1+r_2)^2$.

(D) $(r_1-r_2)^2$.

Question 7. The total surface area (TSA) of a solid frustum of a cone is the sum of its curved surface area and the areas of its two_____

(A) slant heights.

(B) heights.

(C) bases.

(D) vertices.

Question 8. If a cone is cut by a plane parallel to the base, the smaller cone formed at the top is similar to the original cone, meaning the ratio of corresponding lengths (like height, radius, slant height) is_____

(A) squared.

(B) cubed.

(C) constant.

(D) doubled.

Question 9. A common example of a frustum of a cone encountered in daily life is a_____

(A) ball.

(B) box.

(C) bucket.

(D) pipe.

Question 10. If a solid cube is melted and recast into several small spheres, the total volume of all the small spheres will be equal to the volume of the original_____

(A) sphere.

(B) cube.

(C) cylinder.

(D) frustum.