Mensuration MCQs for Competitive Examination
Solve the following problems.
Q. 1
The diagonals of two squares are in the ratio of 3 : 7. What is the ratio of their areas?
(A) 3 : 7
(B) 9 : 49
(C) 9 : 27
(D) 3 : 21
Answer: (B) 9 : 49
Explanation:
Q. 2
The perimeters of a square and a rectangle are equal. If their area be A square meter and B square meter, then the correct statement is
(A) A<B
(B) A≤B
(C) A>B
(D) A≥B
Answer: (C) A>B
Explanation:
Q. 3
What will be the percentage of increase in the area square when each of its sides is increased by 10%?
(A) 20
(B) 11
(C) 121
(D) 21
Answer: (D) 21
Explanation:
Q. 4
Two isosceles triangles have equal vertical angles and their areas are in the ratio of 9 : 16. Then the ratio of their corresponding heights is
(A) 4.5 : 8
(B) 4 : 3
(C) 8 : 4.5
(D) 3 : 4
Answer: (D) 3 : 4
Explanation:
Q. 5
If the area of a circle is A, the radius of the circle is r and the circumference of it is C, then
(A) (A/r)=C
(B) rC=2A
(C) (C/A)=(r/2)
(D) AC=(r²/4)
Answer: (B) rC=2A
Explanation:
Q. 6
In a rhombus ABCD, ∠A = 60° and AB = 12 cm. Then the diagonal BD is
(A) 10 cm
(B) 6 cm
(C) 2√3 cm
(D) 12 cm
Answer: (D) 12 cm
Explanation:
Q. 7
If two medians BE and CF of a triangle ABC, intersect each other at G and if BG = CG, ∠BGC = 60° and BC = 8 cm, then the area of the triangle ABC is
(A) 96√3 cm²
(B) 64√3 cm²
(C) 48√3 cm²
(D) 48 cm²
Answer: (C) 48√3 cm²
Explanation:
Q. 8
Two circles touch each other externally. The sum of their areas is 130 π sq. cm and the distance between their centres is 14 cm. The radius of the smaller circle is
(A) 2 cm
(B) 3 cm
(C) 5 cm
(D) 4 cm
Answer: (D) 4 cm
Explanation:
Q. 9
The time required for a boy to travel along the external and internal boundaries of a circular path are in the ratio 20 : 19. If the width of the path be 5 meters, the internal diameter is
(A) 195
(B) 180
(C) 190
(D) 182
Answer: (D) 182
Explanation:
Q. 10
The area of a circle whose radius is the diagonal of a square whose area is 4 square units is
(A) 16π square units
(B) 4π square units
(C) 6π square units
(D) 8π square units
Answer: (D) 8π square units
Explanation:
Q. 11
The curved surface area of a cylinder is 528 sq cm. If the circumference of its base is 44 cm, find the height of the cylinder?
(A) 12 cm
(B) 24 cm
(C) 36 cm
(D) 6 cm
Answer: (A) 12 cm
Explanation:
Q. 12
A rectangular carpet has an area of 120 m² and a perimeter of 46 metres. The length of its diagonal is
(A) 23 meter
(B) 13 meter
(C) 17 meter
(D) 21 meter
Answer: (C) 17 meter
Explanation;
Q. 13
A plate on a square base made of brass is of length x cm and width 1 mm. The plate weighs 4725 gm. If 1 cubic cm of brass weighs 8.4 gram, then the value of x is
(A) 72
(B) 74
(C) 75
(D) 76
Answer: (C) 75
Explanation:
Q. 14
The length of two parallel sides of a trapezium is 15 cm and 20 cm. If its area is 175 sq. cm, then its height is
(A) 10 cm
(B) 15 cm
(C) 20 cm
(D) 25 cm
Answer: (B) 15 cm
Explanation:
Q. 15
The hypotenuse of a right-angled triangle is 39 cm and the difference of the other two sides is 21 cm. Then, the area of the triangle is
(A) 270 sq. cm
(B) 450 sq. cm
(C) 540 sq. cm
(D) 180 sq. cm
Answer: (A) 270 sq. cm
Explanation:
Q. 16
What is the length of the side of an equilateral triangle, if its area is 64√3 sq cm
(A) 8 cm
(B) 16 cm
(C) 16√3 cm
(D) 8√3 cm
Answer: (B) 16 cm
Explanation:
Q. 17
The area of an equilateral triangle is 9√3 sq cm, find the height of the triangle?
(A) 6 cm
(B) 6√3 cm
(C) 3√3 cm
(D) 9 cm
Answer: (C) 3√3 cm
Explanation:
Q. 18
Points P and Q lie on side AB and AC of triangle ABC respectively such that segment PQ is parallel to side BC. If the ratio of AP : PB is 2:5, and the area of Δ APQ is 4 sq cm, what is the area of trapezium PQCB?
(A) 49 sq cm
(B) 45 sq cm
(C) 25 sq cm
(D) 21 sq cm
Answer: (B) 45 sq. cm
Explanation:
Q. 19
The diameter of a circle is 28 cm. Find its area?
(A) 616 sq cm
(B) 308 sq cm
(C) 154 sq cm
(D) 77 sq cm
Answer: (A) 616 sq. cm
Explanation:
Q. 20
If the radius of a circle is increased by 15% its area increases by
(A) 30 %
(B) 32.25 %
(C) 15 %
(D) 16.125 %
Answer: (B) 32,25 %
Explanation: