MCQs with Solutions for all Competitive Examinations

Mensuration MCQs for Competitive Examination

Solve the following problems.

Q. 21
The volume of a right circular cone is 924 cm³. If its height is 18 cm, then the area of its base (in cm²) is

(A) 132
(B) 198 
(C) 176 
(D) 154 

Answer: (D) 154

Q. 22
The area of a field in the shape of a hexagon is 2400√3 m². What will be the cost of fencing it at Rs. 18.50 per metre?

(A) Rs. 4440
(B) Rs. 5920
(C) Rs. 5550
(D) Rs. 5180

Answer: (A) Rs. 4440

Q. 23
The curved surface area and the volume of a cylindrical pole are 132 m² and 528 m³, respectively. What is the height (in meter) of the pole? (Take π = 22/7)

(A) 2(1/2)
(B) 3(5/8)
(C) 3(1/2)
(D) 2(5/8)

Answer: (D) 2(5/8)

Q. 24
The radius of the base of a cylinder is 7 cm and its curved surface area is 440 cm². Its volume (in cm³ ) will be (Take  π = 22/7)

(A) 1760
(B) 1430
(C) 1540
(D) 1650

Answer: (C) 1540

Q. 25
A circle circumscribes a rectangle whose sides are in the ratio 4 : 3. If the perimeter of the rectangle is 56 cm, then what is the area (in cm²) of the circle?

(A) 70π
(B) 96π
(C) 90π
(D) 100π

Answer: (D) 100π

Q. 26
The perimeter of two similar triangles ΔABC and ΔPQR is 36 cms and 24 cms respectively. If PQ = 10 cm then the length of AB is

(A) 18 cm
(B) 12 cm
(C) 15 cm
(D) 30 cm

Answer: (C) 15 cm

Q. 27
What is the area of a rhombus (in cm²) whose side is 10 cm and the smaller diagonal is 12 cm?

(A) 120
(B) 192
(C) 96
(D) 50

Answer: (C) 96

Q. 28
The diameters of two cylinders are in the ratio 3 : 2 and their volumes are equal.  The ratio of their heights is

(A) 2 : 3
(B) 3 : 2
(C) 9 : 4
(D) 4 : 9

Answer: (D) 4 : 9

Q. 29
A circle inscribed in a triangle ABC. It touches sides AB, BC and AC at the points P, Q and R respectively. If BP = 9 cm. CQ = 10 cm and AR = 11 cm, then the perimeter (in cm) of the ∆ABC is

(A) 57.5
(B) 72.5
(C) 60
(D) 75

Answer: (C) 60

Q. 30
In triangle ABC, the length of BC is less than twice the length of AB by 2cm. The length of AC exceeds the length of AB by 10 cm. The perimeter is 32 cm. The length (in cm) of the smallest side of the triangle is

(A) 4
(B) 6
(C) 8
(D) 10

Answer: (B) 6

Q. 31
If each side of a rectangle is increased by 22% then its area will increase by

(A) 44%
(B) 50%
(C) 46.65%
(D) 48.84%

Answer: (D) 48.84%

Q. 32
The diagonals of a rhombus are respectively 4 cm and 12 cm. Its area (in cm²) is equal to

(A) 8
(B) 36
(C) 12
(D) 24

Answer: (D) 24
Explanation: Area = (1/2)(product of the two diagonals)

Q. 33
The area of the largest triangle that can be inscribed in a semicircle of radius 6m is

(A) 36 m2
(B) 72 m2
(C) 18 m2
(D) 12 m2

Answer: (A) 36 m²

Q. 34
Equilateral triangles are drawn on the hypotenuse and one of the perpendicular sides of a right-angled isosceles triangles. Their areas are H and A respectively. A/H is equal to

(A) 1/4
(B) 1/√2
(C) 1/2
(D) 1/2√2

Answer: (C) 1/2

Q. 35
O, G, I and H are respectively the circumcentre, centroid, incentre and orthocentre of an equilateral triangle. Which of these points are identical?

(A) O and I only
(B) O, G, I and H
(C) O and G only
(D) O, G and H only

Answer: (B) O, G, I and H
Explanation: (In an equilateral triangle the circumcentre, centroid, incentre and orthocentre are the same point) 

Q. 36
If the height of the equilateral triangle is 2√3 cm, then determine the area (in cm²) of the equilateral triangle

(A) 6
(B) 2√3
(C) 4√3
(D) 12

Answer: (C) 4√3

Q. 37
Length and breadth of a rectangle are increased by 10% and 20% respectively. What will be the percentage increase in the area of the rectangle?

(A) 30%
(B) 32%
(C) 28%
(D) 33%

Answer: (B) 32%

Q. 38
If the length of one side and the diagonal of a rectangle are 7 cm and 25 cm respectively, then find its perimeter (in cm)

(A) 124
(B) 36
(C) 62
(D) 72

Answer: (C) 62

Q. 39
The side of an equilateral triangle is 8 cm. Find its area (in cm²)

(A) 25√3
(B) 16√2
(C) 28√2
(D) 16√3

Answer: (D) 16√3

Q. 40
The area of a circle is 346.5 cm². Find its circumference (in cm).

(A) 132
(B) 38
(C) 66
(D) 76

Answer: (C) 66

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