MCQs with Solutions for all Competitive Examinations

Mensuration MCQs for Competitive Examination

Solve the following problems.

Q. 81
The base angle of an isosceles trapezium is 45°. If the shorter side and both the equal sides are 10 cm each, what is the area of the trapezium?

(A) 50√2 + 50 cm²
(B) 50√2 + 100 cm²
(C) 100√2 + 50 cm²
(D) 100√2 + 100 cm²

Answer: (A) 50√2 + 50 cm²

Q. 82
If the radius  of a circle is increased by 27%, then its area will increase by

(A) 61.29 %
(B) 54 %
(C) 27 %
(D) 30.645 %

Answer: (A) 61.29 %

Q. 83
The curved surface area of a hemisphere is 2772 sq cm and volume is 19404  cubic cm, what is its radius? (Take π = 22/7)

(A) 42 cm
(B) 21 cm
(C) 10.5 cm
(D) 31.5 cm

Answer: (B) 21 cm

Q. 84
ΔDEF and ΔGHI are similar triangles. Length of DE is 4 cm and length of the corresponding side GH is 9 cm. What is the ratio of areas of ΔDEF and ΔDEF?

(A) 81 : 16
(B) 4 : 9
(C) 16 : 81
(D) 9 : 4

Answer: (C) 16 : 81

Q. 85
 Find the radius of the circle if the length of its arc is 33 cm whose corresponding central angle is 90°

(A) 21 cm
(B) 14 cm
(C) 7 cm
(D) 28 cm

Answer: (A) 21 cm

Q. 86
A cylindrical vessel of radius 6 cm is partially filled with water. By how much will the water level rise if a sphere of radius 5 cm is completely immersed in this water? (Take π = 22/7)

(A) 6.67  cm
(B) 5.56  cm
(C) 6.94  cm
(D) 4.63  cm

Answer: (D) 4.63 cm

Q. 87
What is the total surface area (in sq cm) of a hollow cylinder open at both ends, if its length is 22 cm, external radius is 7 cm and thickness is 1 cm? (Take π = 22/7)

(A) 1879.43
(B) 3758.86
(C) 939.715
(D) 2819.145

Answer: (A) 1879.43

Q. 88
If a cylinder of radius 4.3 cm and height 4.8 cm is melted and constructed into a cone of the same radius, what will be the height of this cone? (Use π =22/7)

(A) 28.8 cm
(B) 14.4 cm
(C) 7.2 cm
(D) 21.6 cm

Answer: (B) 14.4 cm

Q. 89
What is the length of the side of a regular hexagon, if its area is 54√3 sq cm?

(A) 12 cm
(B) 9 cm
(C) 6 cm
(D) 15 cm

Answer: (C) 6 cm

Q. 90
The perimeters of a square and an equilateral triangle are equal. If the diagonal of the square is 9 cm, what is the area of the equilateral triangle?

(A) 18√3 sq cm
(B) 9√3 sq cm
(C) 18√2 sq cm
(D) 9√2 sq cm

Answer: (A) 18√3 sq cm

Q. 91
The total surface area of a cuboid is 376 sq cm. Find its volume if its length and breadth are 10 cm and 8 cm respectively?

(A) 960 cm³
(B) 240 cm³
(C) 480 cm³
(D) 720 cm³

Answer: (C) 480 cm³

Q. 92
A circular swimming pool is surrounded by a concrete wall 4m wide. If the area of the concrete wall surrounding the pool is 11/25 that of the pool, then the radius (in m) of the pool is

(A) 8
(B) 20
(C) 16
(D) 30

Answer: (B) 20
Explanation: Radius of the swimming pool = R(say)
Radius of the pool with the wall = (R + 4)
π[(R + 4)² – R²] = (11/25)*π*R²

Q. 93
A cylindrical capsule has  hemispherical ends of the radii equal to radius  of the cylindrical part. If length of the capsule is 40 m and radius  6 m, what is the total surface area of this capsule?

(A) 3017.14 m²
(B) 4525.71 m²
(C) 1508.57 m²
(D) 754.29  m²

Answer: (C) 1508.57 m²

Q. 94
A solid right circular cone of radius 10 cm and height 8 cm is put inside a cylindrical vessel of radius 11 cm and height 9 cm. How much water in cubic cm will be required to fill the cylindrical vessel completely?

(A) 5168.96 cm³
(B) 2584.48 cm³
(C) 7753.44 cm³
(D) 1292.24 cm³

Answer: (B) 2584.48 cm³

Q. 95
A cylindrical vessel of height 9 cm and radius 7 cm is completely filled with sand. When this sand is poured out it forms a right circular cone of radius  10 cm what will be the height of this cone?

(A) 26.46 cm
(B) 39.69 cm
(C) 13.23 cm
(D) 52.92 cm

Answer: (C) 13.22 cm

Q. 96
Area of the circle inscribed in a square of diagonal 6√2 cm (in sq cm) is 

(A) 9 π
(B) 6 π
(C) 3 π
(D) 9√2π

Answer: (A) 9 π

Q. 97
The diagonals of two squares are in the ratio 5 : 2.The ratio of their area is

(A) 5 : 6
(B) 25 : 4
(C) 5 : 4
(D) 125 : 8

Answer: (B) 25 : 4

Q. 98
Two adjacent sides of a parallelogram are 21 cms and 20 cms. The diagonal joining the endpoints of these two sides is 29 cms. The area of the parallelogram (in sq. cms) is

(A) 240
(B) 120
(C) 210
(D) 420

Answer: (D) 420

Q. 99
A sphere has the same curved surface area as a cone of vertical height 40 cm and radius 30 cm. The radius of the sphere is

(A) 5√5 cm
(B) 5√3 cm
(C) 5√15 cm
(D) 5√10 cm

Answer: (C) 5√15 cm

Q. 100
The diameter of a sphere is twice the diameter of another sphere. The curved surface area of the first and the volume of the second are numerically equal. The numerical value of the radius of the first sphere is

(A) 3
(B) 24
(C) 8
(D) 16

Answer: (B) 24

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