Matching Items MCQs for Sub-Topics of Topic 7: Mensuration

(i) Mensuration

(ii) Perimeter

(iii) Area

(iv) Volume

(a) Measure of the capacity of a 3D object

(b) Measure of the boundary of a 2D shape

(c) Measure of the surface enclosed by a 2D shape

(d) Measurement of geometric figures

(i) Length

(ii) Area

(iii) Volume

(iv) Circumference

(a) $\text{m}^3$

(b) $\text{cm}^2$

(c) $\text{km}$

(d) $\text{mm}$

(i) Perimeter

(ii) Area

(iii) Side

(iv) Capacity

(a) Amount of surface

(b) One-dimensional measure

(c) Boundary length

(d) Space inside a container

(i) Cost of painting a wall

(ii) Cost of buying wire for a fence

(iii) Cost of filling a pool

(iv) Cost of tiling a roof

(a) Volume

(b) Surface Area (on solid)

(c) Perimeter

(d) Area (on plane)

(i) Square

(ii) Cube

(iii) Triangle

(iv) Sphere

(a) Volume/Surface Area

(b) Perimeter/Area

(c) Perimeter/Area

(d) Volume/Surface Area

(i) Polygon

(ii) Square

(iii) Rectangle

(iv) Equilateral Triangle

(a) Sum of lengths of all sides

(b) $4 \times$ side length

(c) $2 \times$ (length + width)

(d) $3 \times$ side length

(i) Square, side 8 cm

(ii) Rectangle, length 10 m, width 5 m

(iii) Triangle, sides 6 cm, 8 cm, 10 cm

(iv) Parallelogram, adjacent sides 7 m, 4 m

(a) 22 m

(b) 24 cm

(c) 32 cm

(d) 30 m

(i) Doubling the side of a square

(ii) Doubling the length and width of a rectangle

(iii) Halving the side of an equilateral triangle

(iv) Keeping perimeter constant but changing shape from square to rectangle

(a) Perimeter is halved

(b) Perimeter remains unchanged (potentially)

(c) Perimeter is doubled

(d) Perimeter is doubled

(i) Boundary

(ii) Regular polygon

(iii) Circumference

(iv) Semi-perimeter

(a) Half of the perimeter of a triangle

(b) The perimeter of a circle

(c) All sides and angles are equal

(d) The outer limit of a shape

(i) Square with side $s$

(ii) Rectangle with length $l$ and width $w$

(iii) Triangle with sides $a, b, c$

(iv) Parallelogram with adjacent sides $p, q$

(a) $2(p+q)$

(b) $a+b+c$

(c) $2(l+w)$

(d) $4s$

(i) Square

(ii) Rectangle

(iii) Triangle

(iv) Parallelogram

(a) $b \times h$

(b) $s^2$

(c) $l \times w$

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

(i) Square, side 7 cm

(ii) Rectangle, length 12 m, width 8 m

(iii) Triangle, base 10 cm, height 6 cm

(iv) Parallelogram, base 9 m, height 5 m

(a) $45\ \text{m}^2$

(b) $96\ \text{m}^2$

(c) $49\ \text{cm}^2$

(d) $30\ \text{cm}^2$

(i) Doubling the side of a square

(ii) Doubling the length and width of a rectangle

(iii) Doubling the base of a triangle while keeping height same

(iv) Halving the base and height of a parallelogram

(a) Area is halved

(b) Area becomes four times

(c) Area is doubled

(d) Area becomes one-fourth

(i) Area of a stamp

(ii) Area of a room floor

(iii) Area of a small field

(iv) Area of a country

(a) $\text{km}^2$

(b) $\text{m}^2$

(c) $\text{cm}^2$

(d) Hectare

(i) Area of a square

(ii) Area of a rectangle

(iii) Area of a right triangle

(iv) Area of a parallelogram

(a) base $\times$ height

(b) $\frac{1}{2} \times$ product of perpendicular sides

(c) side $\times$ side

(d) length $\times$ width

(i) $a, b, c$

(ii) $s$

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

(iv) $a+b+c$

(a) Perimeter of the triangle

(b) Area of the triangle

(c) Lengths of the sides

(d) Semi-perimeter of the triangle

(i) Scalene Triangle

(ii) Equilateral Triangle

(iii) Isosceles Triangle

(iv) Right-angled Triangle

(a) $\sqrt{s(s-a)(s-a)(s-c)}$

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

(c) $\sqrt{s(s-a)(s-a)(s-a)}$

(d) Can be used, but base $\times$ height is simpler

(i) 6, 8, 10

(ii) 5, 12, 13

(iii) 7, 15, 20

(iv) 10, 10, 16

(a) 18

(b) 16

(c) 12

(d) 15

(i) 3, 4, 5

(ii) 5, 12, 13

(iii) 7, 8, 9

(iv) 13, 14, 15

(a) 6

(b) 84

(c) $12\sqrt{5}$

(d) 30

(i) Equilateral triangle, side $a$

(ii) Right triangle, legs $b, h$

(iii) Triangle, base $b$, height $h$

(iv) Isosceles right triangle, leg $a$

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

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

(c) $\frac{1}{2}a^2$

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

(i) Rhombus

(ii) Kite

(iii) General Quadrilateral (with diagonal $d$, perpendiculars $h_1, h_2$)

(iv) Trapezium (parallel sides $a, b$, height $h$)

(a) $\frac{1}{2} d_1 d_2$

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

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

(d) $\frac{1}{2} d_1 d_2$

(i) Rhombus, diagonals 10 cm, 16 cm

(ii) Kite, diagonals 12 m, 15 m

(iii) Trapezium, parallel sides 8 cm, 14 cm, height 5 cm

(iv) Quadrilateral, diagonal 20 m, perpendiculars 7 m, 9 m

(a) $60\ \text{cm}^2$

(b) $90\ \text{m}^2$

(c) $80\ \text{cm}^2$

(d) $160\ \text{m}^2$

(i) Triangulation

(ii) Using a diagonal and perpendiculars

(iii) Using properties of regular polygons

(iv) Using Heron's formula

(a) Divide into triangles from one vertex

(b) Sum area of triangles formed by a diagonal

(c) Using semi-perimeter and side lengths of triangles

(d) Divide into congruent isosceles triangles meeting at the center

(i) Diagonals are perpendicular

(ii) Opposite sides are parallel

(iii) Exactly one pair of parallel sides

(iv) All sides are equal, diagonals are perpendicular

(a) Trapezium

(b) Parallelogram

(c) Rhombus

(d) Rhombus or Kite

(i) Regular Pentagon

(ii) Regular Hexagon

(iii) Regular Octagon

(iv) Regular Decagon

(a) 10

(b) 5

(c) 8

(d) 6

(i) Circumference

(ii) Area

(iii) Diameter

(iv) Relationship between A and C

(a) $2r$

(b) $2\pi r$

(c) $A = \frac{Cr}{2}$

(d) $\pi r^2$

(i) Radius 7 cm

(ii) Diameter 14 m

(iii) Radius 21 mm

(iv) Diameter 42 cm

(a) 44 m

(b) 132 mm

(c) 44 cm

(d) 132 cm

(i) Radius 7 cm

(ii) Diameter 14 m

(iii) Radius 21 mm

(iv) Diameter 42 cm

(a) $154\ \text{m}^2$

(b) $1386\ \text{cm}^2$

(c) $154\ \text{cm}^2$

(d) $1386\ \text{mm}^2$

(i) Radius is doubled

(ii) Diameter is tripled

(iii) Radius is halved

(iv) Diameter is quartered

(a) Circumference is halved

(b) Area becomes nine times

(c) Circumference is doubled

(d) Area becomes one-sixteenth

(i) Circumference

(ii) Area

(iii) Radius

(iv) Ratio of circumference to diameter

(a) Pi ($\pi$)

(b) Space covered by a circular carpet

(c) Distance a wheel travels in one rotation

(d) Distance from the center to the boundary

(i) Sector

(ii) Segment

(iii) Minor Sector

(iv) Major Segment

(a) Region bounded by an arc and a chord

(b) Region bounded by two radii and an arc

(c) The larger segment formed by a chord

(d) Sector with a central angle less than 180 degrees

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

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

(iii) $2r + l$

(iv) $\frac{1}{2} r l$

(a) Area of a sector

(b) Length of an arc

(c) Perimeter of a sector

(d) Area of a sector (using arc length)

(i) Central angle $90^\circ$

(ii) Central angle $180^\circ$

(iii) Central angle $120^\circ$

(iv) Central angle $45^\circ$

(a) $1/8$th of the circle area

(b) $1/4$th of the circle area

(c) $1/2$th of the circle area

(d) $1/3$rd of the circle area

(i) Area of Minor Segment

(ii) Area of Major Segment

(iii) Area of triangle in sector

(iv) Area of corresponding sector

(a) $\frac{1}{2} r^2 \sin \theta$ (for angle $\theta$)

(b) Area of circle - Area of minor segment

(c) $\frac{\theta}{360} \pi r^2$

(d) Area of sector - Area of triangle

(i) Arc length, r=10, $\theta=90^\circ$

(ii) Area of sector, r=10, $\theta=90^\circ$

(iii) Area of triangle in sector, r=10, $\theta=90^\circ$

(iv) Area of minor segment, r=10, $\theta=90^\circ$

(a) 50

(b) 78.5

(c) 15.7

(d) 28.5

(i) Figure formed by non-overlapping shapes

(ii) Figure with a shape removed from within another

(iii) Path around a rectangle (outside)

(iv) Path inside a square (along boundary)

(a) Area of larger outer shape - Area of smaller inner shape

(b) Sum of areas of individual shapes

(c) Area of inner shape - Area of remaining part (Incorrect phrasing)

(d) Area of outer rectangle - Area of inner rectangle

(i) Two squares joined along one side

(ii) Rectangle with a semicircle on one side

(iii) Circular track (ring)

(iv) Square with a square hole in the middle

(a) Sum of outer boundary lengths

(b) Circumference of outer circle + Circumference of inner circle

(c) Sum of 3 sides of rectangle + Arc length of semicircle

(d) Sum of 6 sides of the original squares

(i) Path crossing rectangular park

(ii) Circle inscribed in a square

(iii) Square inscribed in a circle

(iv) Semicircles on sides of right triangle

(a) Area of square - Area of circle (Space between)

(b) Overlapping area is subtracted

(c) Related to area of the triangle itself (Lunes of Hippocrates)

(d) Area of circle - Area of square (Space between)

(i) Side of inner square

(ii) Area of outer square

(iii) Area of inner square

(iv) Area of the path

(a) $1600\ \text{m}^2$

(b) $900\ \text{m}^2$

(c) $30\ \text{m}$

(d) $2500\ \text{m}^2$

(i) Square with two semicircles on opposite sides

(ii) Rectangle with four quadrants at corners

(iii) Circle with a square hole

(iv) Two circles touching externally

(a) Two arcs and four straight lines

(b) Two arcs and two straight lines

(c) One arc (circumference)

(d) Two arcs (circumferences)

(i) Face

(ii) Edge

(iii) Vertex

(iv) Solid

(a) Point where edges meet

(b) Three-dimensional figure

(c) Flat or curved surface

(d) Line segment where faces meet

(i) Cube

(ii) Cylinder

(iii) Pyramid

(iv) Sphere

(a) Round solid

(b) Polyhedron with square faces

(c) Two circular bases and curved surface

(d) Polygonal base and triangular sides meeting at apex

(i) Cube

(ii) Square Pyramid

(iii) Triangular Prism

(iv) Sphere

(a) 5

(b) 1

(c) 5

(d) 6

(i) Cuboid

(ii) Cone

(iii) Triangular Prism

(iv) Cylinder

(a) 0

(b) 6

(c) 1

(d) 8

(i) Cube

(ii) Square Pyramid

(iii) Cylinder

(iv) Cone

(a) 1

(b) 8

(c) 12

(d) 2

(i) Total Surface Area (TSA)

(ii) Lateral Surface Area (LSA)

(iii) Area of Base

(iv) Area of Top

(a) Area of the bottom face

(b) Sum of the areas of all six faces

(c) Sum of the areas of the four vertical faces

(d) Area of the face opposite to the base

(i) Cube

(ii) Cuboid

(iii) Cylinder

(iv) Cone

(a) $4s^2$

(b) $\pi r l$

(c) $2\pi r h$

(d) $2(l+w)h$

(i) Cube

(ii) Cuboid

(iii) Solid Cylinder

(iv) Solid Cone

(a) $6s^2$

(b) $\pi r (r+l)$

(c) $2(lw+wh+hl)$

(d) $2\pi r (r+h)$

(i) Sphere

(ii) Hemisphere (Curved Surface Area)

(iii) Hemisphere (Total Surface Area)

(iv) Spherical Shell (Outer Surface Area)

(a) $4\pi r^2$

(b) $2\pi r^2$

(c) $3\pi r^2$

(d) $4\pi r^2$ (Assuming $r$ is the outer radius)

(i) Side/Radius doubled

(ii) Side/Radius tripled

(iii) Side/Radius halved

(iv) Side/Radius is $n$ times

(a) Surface area becomes $n^2$ times

(b) Surface area becomes $1/4$ times

(c) Surface area becomes 4 times

(d) Surface area becomes 9 times

(i) Cube

(ii) Cuboid

(iii) Cylinder

(iv) Cone

(a) $\pi r^2 h$

(b) $s^3$

(c) $lwh$

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

(i) Sphere

(ii) Hemisphere

(iii) Spherical Shell (Volume of material, outer radius $R$, inner radius $r$)

(iv) Relationship between Sphere V and Hemisphere V

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

(b) $V_{sphere} = 2 \times V_{hemisphere}$

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

(d) $\frac{4}{3}\pi (R^3 - r^3)$

(i) Cube, side 10 cm

(ii) Cuboid, 8 cm $\times$ 5 cm $\times$ 4 cm

(iii) Cylinder, radius 7 cm, height 10 cm

(iv) Cone, radius 6 cm, height 7 cm

(a) $160\ \text{cm}^3$

(b) $1540\ \text{cm}^3$

(c) $264\ \text{cm}^3$

(d) $1000\ \text{cm}^3$

(i) Side/Radius doubled

(ii) Side/Radius tripled

(iii) Side/Radius halved

(iv) Side/Radius is $n$ times

(a) Volume becomes $1/8$ times

(b) Volume becomes 8 times

(c) Volume becomes 27 times

(d) Volume becomes $n^3$ times

(i) Volume of a water tank

(ii) Volume of earth from a well

(iii) Volume of air in a room

(iv) Volume of a solid object

(a) Space occupied by the object

(b) Capacity for liquid

(c) Space for living/working

(d) Material removed from excavation

(i) Cone on a Hemisphere

(ii) Cylinder with Hemispherical ends

(iii) Cylinder with Cone removed from top

(iv) Cube with Hemisphere on top

(a) CSA of cylinder + CSA of two hemispheres

(b) 5 faces of cube + CSA of hemisphere + (Area of cube top - Area of hemisphere base)

(c) CSA of cone + CSA of hemisphere

(d) CSA of cylinder + Area of cylinder base + CSA of cone

(i) Cone on a Hemisphere

(ii) Cylinder with Hemispherical ends

(iii) Sphere removed from Cylinder

(iv) Cylinder and Cone on same base

(a) Volume of Cylinder + Volume of Cone

(b) Volume of Cylinder - Volume of Sphere

(c) Volume of Cone + Volume of Hemisphere

(d) Volume of Cylinder + 2 $\times$ Volume of Hemisphere

(i) Toy: cone on hemisphere (same radius)

(ii) Capsule: cylinder with hemispherical ends (same radius)

(iii) Bird-bath: cylinder with hemispherical depression (same radius)

(iv) Pencil: cylinder with conical tip

(a) Volume is Volume of Cylinder - Volume of Hemisphere

(b) Total Surface Area is CSA of Cylinder + CSA of 2 Hemispheres

(c) Total Volume is Volume of Cylinder + Volume of Cone

(d) Joint surface area (circle) is excluded from TSA sum

(i) Toy: Cone on Hemisphere, diameter 7 cm, cone height 10 cm

(ii) Capsule: length 14 mm, diameter 5 mm

(iii) Solid: Cylinder (H=19, D=7) with hemispherical ends

(iv) Wooden article: Cylinder (H=10, R=3.5) with hemispheres scooped out

(a) Radius of hemisphere = 2.5 mm

(b) Radius of hemisphere = 3.5 cm

(c) Height of cylinder = 9 mm

(d) Height of cylinder = 12 cm

(i) Volume of Cylinder + Volume of Hemisphere

(ii) Volume of Cylinder - Volume of Hemisphere

(iii) Volume of Cube + Volume of Cone

(iv) Volume of Cylinder + 2 $\times$ Volume of Hemisphere

(a) Solid with hemispherical depression at one end of cylinder

(b) Solid with hemispherical ends on a cylinder

(c) Solid cube with cone on top

(d) Solid cone on a hemisphere

(i) Melting and recasting a solid

(ii) Digging earth from a well and spreading it

(iii) Drawing a wire from a solid cylinder

(iv) Reshaping clay into a different form

(a) Volume of material

(b) Volume of excavated material = Volume of spread material

(c) Volume of original shape = Volume of new shape

(d) Volume remains constant

(i) Volume

(ii) Curved Surface Area

(iii) Area of Top Base

(iv) Slant Height

(a) $\pi r_2^2$ (assuming $r_2$ is top radius)

(b) $\pi (r_1+r_2)l$

(c) $\sqrt{h^2 + (r_1-r_2)^2}$

(d) $\frac{1}{3}\pi h (r_1^2 + r_2^2 + r_1 r_2)$

(i) Difference in radii ($r_1-r_2$)

(ii) Square of difference in radii

(iii) Square of height

(iv) Slant height

(a) 576

(b) 49

(c) 7

(d) 25

(i) Upper part

(ii) Lower part

(iii) Sectional plane

(iv) Base of the original cone

(a) A circle parallel to the original base

(b) A smaller cone

(c) A frustum

(d) A circular base

(i) Recast into a cylinder of height 9 cm

(ii) Recast into 27 smaller spheres

(iii) Recast into a cone with radius 4 cm

(iv) Recast into a hemisphere

(a) $\frac{4}{3}\pi 3^3 = 27 \times \frac{4}{3}\pi r_{new}^3 \implies r_{new} = 1\ \text{cm}$

(b) $\frac{4}{3}\pi 3^3 = \pi r_{cylinder}^2 \times 9 \implies r_{cylinder} = 2\ \text{cm}$

(c) $\frac{4}{3}\pi 3^3 = \frac{2}{3}\pi r_{hemi}^3 \implies r_{hemi} = 3\sqrt[3]{2}\ \text{cm}$

(d) $\frac{4}{3}\pi 3^3 = \frac{1}{3}\pi 4^2 h_{cone} \implies h_{cone} = 6.75\ \text{cm}$