Mensuration MCQs for Competitive Examination
Solve the following problems.
Q. 61
If in-radius of an equilateral triangle is 3 cm. Calculate the perimeter (in m) of the equilateral triangle.
(A) 6√3
(B) 3√3
(C) 12√3
(D) 18√3
Answer: (D) 18√3
Explanation:
Q. 62
Find the curved surface area (in cm²) of a right circular cylinder of diameter 14 cm and height 8 cm.
(A) 308
(B) 352
(C) 327
(D) 371
Answer: (B) 352
Explanation:
Q. 63
The perimeter and the length of one of the diagonals of a rhombus is 26 cm and 5 cm respectively. Find the length of its other diagonal (in cm).
(A) 6
(B) 12
(C) 24
(D) 18
Answer: (B) 12
Explanation:
Q. 64
The total surface area of a cube is 253.5 cm². Find its side (in cm).
(A) 7.5
(B) 5.5
(C) 6.5
(D) 8.5
Answer: (C) 6.5
Explanation:
Q. 65
The volume of a hemisphere is 89.83 cm³. Find its diameter (in cm).
(A) 3.5
(B) 7
(C) 14
(D) 10.5
Answer: (B) 7
Explanation:
Q. 66
The diagonal of a quadrilateral shaped field is 24 m and the perpendicular dropped on it from the remaining opposite vertices are 8 m and 13 m. The area of the field is
(A) 252 m²
(B) 156 m²
(C) 96 m²
(D) 1152 m²
Answer: (A) 252 m²
Explanation:
Q. 67
In ΔABC, a line through A cuts the side BC at D such that BD : DC = 4 : 5. If the area of ΔABD = 60 cm², then the area of ΔADC is
(A) 90 cm²
(B) 50 cm²
(C) 60 cm²
(D) 75 cm²
Answer: (D) 75 cm²
Explanation: BD= 4x, DC= 5x
Take ‘h’ as the height of both ΔABD and ΔADC. Then use (1/2)(base)(altitude) formula for both the triangles.
Q. 68
If the area of the base, height and volume of a right prism be (3√3/ 2) P2 cm2, 100√3 cm and 7200 cm3 respectively, then the value of P will be
(A) 2√3
(B) √3
(C) 3/2
(D) 4
Answer: (D) 4
Explanation: Volume of right prism = (Area of the base * Height)
Q. 69
ΔABC is similar to ΔDEF. The ratio of their perimeters is 4 : 1. The ratio of their areas is
(A) 4 : 1
(B) 16 : 1
(C) 8 : 1
(D) 8 2 : 1
Answer: (B) 16 : 1
Explanation:
Q. 70
The amount of rice produced in a square field of side 50 m is 750 kg. The amount of rice produced in a similar square field of side 100 m will be
(A) 2000 kg
(B) 3000 kg
(C) 3500 kg
(D) 1500 kg
Answer: (B) 3000 kg
Explanation:
Q. 71
Two triangles ABC and PQR are congruent. If the area of ΔABC is 60 sq. cm, then the area of ΔPQR will be
(A) 30 cm²
(B) 60 cm²
(C) 55 cm²
(D) 66 cm²
Answer: (B) 60 cm²
Explanation:
Q. 72
A wire of length 44 cm is first bent to form a circle and then re-bent to form a square. The difference of the two enclosed areas is
(A) 44
(B) 33
(C) 22
(D) 55
Answer: (B) 33
Explanation;
Q. 73
A parallelogram has sides 60 m and 40 m and one of its diagonals is 80 m long. Its area is
(A) 500 √15 m²
(B) 600 √15 m²
(C) 400 √15 m²
(D) 450 √15 m²
Answer: (B) 600 √15 m²
Explanation:
Q. 74
The area of a regular hexagon with side ‘a’ is
(A) ((3√3)/4)a² square unit
(B) (12/2√3)a² square unit
(C) (9/2√3)a² square unit
(D) (3√3/2)a² square unit
Answer: (D) (3√3/2)a² square unit
Explanation:
Q. 75
The lengths of two parallel sides of a trapezium are 6 cm and 8 cm. If the height of the trapezium be 4 cm, then its area is
(A) 28 sq cm
(B) 56 sq cm
(C) 30 sq cm
(D) 32 sq cm
Answer: (A) 28 sq cm
Explanation:
Q. 76
If the ratio of the altitudes of two triangles be 3 : 4 and the ratio of their corresponding areas be 4 : 3, then the ratio of their corresponding lengths of bases is
(A) 1 : 1
(B) 16 : 9
(C) 1 : 2
(D) 2 : 1
Answer: (B) 16 : 9
Explanation:
Q. 77
The length and breadth of a square are increased by 30% and 20% respectively. The area of the rectangle so formed exceeds the area of the square by
(A) 58.4%
(B) 66%
(C) 42%
(D) 56%
Answer: (D) 56%
Explanation:
Q. 78
If each edge of a cube is increased by 40%, the percentage increase in its surface area is
(A) 40%
(B) 60%
(C) 80%
(D) 96%
Answer: (D) 96%
Explanation:
Q. 79
One side of a square is increased by 30%. To maintain the same area, the other side will have to be decreased by
(A) 23(1/13)%
(B) 76(12/13)%
(C) 30%
(D) 15%
Answer: (A) 23(1/13)%
Explanation:
Q. 80
If the perimeters of a rectangle and a square are equal and the ratio of two adjacent sides of the rectangle is 1 : 2 then the ratio of the area of the rectangle and that of the square is
(A) 1 : 1
(B) 1 : 2
(C) 2 : 3
(D) 8 : 9
Answer: (D) 8 : 9
Explanation: