Free Area and Volume MCQs with Answers
204 Area and Volume MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Area measures the surface enclosed by two-dimensional figures, while volume measures the space occupied by three-dimensional solids. Problems use formulas for rectangles, triangles, circles, prisms, cylinders, cones, spheres, and composite figures, including unit conversion and the distinction between surface area, lateral area, and volume.
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204 questions · page 2 of 11
- A. 15 m
- B. 16 m
- C. 17 m
- D. 20 m
Explanation: The perimeter gives L + B = 46 metres ÷ 2 = 23 metres, and the area gives LB = 120 square metres.
Correct answer: 17 m- A. 480 sq.m
- B. 320 sq.m
- C. 600√15 sq.m
- D. 450√15
Explanation: For the diagonal of 80 metres, the cosine rule gives 80² = 60² + 40² − 2 × 60 × 40 cos θ, so cos θ = 1/4.
Correct answer: 600√15 sq.m- A. 24 cm,48cm
- B. 12cm,24cm
- C. 6√2cm,12√2cm
- D. 6cm,12cm
Explanation: The area of a rhombus is half the product of its diagonals. Let the shorter diagonal be d centimetres, so the longer one is 2d…
Correct answer: 12cm,24cm- A. 56m
- B. 64m
- C. 88m
- D. 168m
Explanation: The grazing area is a circle with area πr² = 9856 square metres. Using π = 22/7, r² = 9856 square metres × 7/22 = 3136 square metres, so r…
Correct answer: 56m25. The diameter of a circle is 105 cm less than the circumference what is the diameter of the circle?
- A. 44 cm
- B. 46 cm
- C. 48 cm
- D. 49 cm
Explanation: Using circumference C = πd, we have πd - d = 105 cm, so (22/7 - 1)d = 105 cm.
Correct answer: 49 cm- A. 1000
- B. 1500
- C. 1700
- D. 2000
Explanation: The wheel's circumference is πd = (22/7) × (7/11) m = 2 m per revolution.
Correct answer: 2000- A. 30 cm
- B. 60 cm
- C. 72 cm
- D. 132 cm
Explanation: The wire length is the circle's circumference: 2πr = 2 × (22/7) × 42 cm = 264 cm.
Correct answer: 60 cm- A. 100%
- B. 200%
- C. 300%
- D. 400%
Explanation: Increasing the diameter by 100% makes it twice its original value, so the radius also becomes twice as large.
Correct answer: 300%- A. 25 %
- B. 50%
- C. 75%
- D. 100%
Explanation: Reducing the radius by 50% leaves a radius of 0.5r. The new area is π(0.5r)² = 0.25πr², so 25% remains and the reduction is 100% - 25% =…
Correct answer: 75%- A. 9856
- B. 8956
- C. 6589
- D. 5986
Explanation: From C = 2πr, the radius is r = 352 m ÷ (2 × 22/7) = 56 m. Therefore the area is πr² = (22/7) × (56 m)² = 9856 m²; option b, 8956 m²…
Correct answer: 9856- A. x/2
- B. x
- C. 2x
- D. 4x
Explanation: The square has area x² square units, while the triangle has area 1/2 × x × h square units.
Correct answer: 2x- A. Becomes fourfold
- B. Becomes threefold
- C. Becomes twofold
- D. none of the above
Explanation: For a square, diagonal d = side × √2, so doubling the diagonal also doubles the side.
Correct answer: Becomes fourfold- A. 9 1/11 %
- B. 10%
- C. 11%
- D. 11 1/9 %
Explanation: If the base becomes 110% of its original value, the altitude must become 100/110 = 10/11 of its original value to keep the area unchanged.
Correct answer: 9 1/11 %- A. 1
- B. 2
- C. 4
- D. Data Inadequate
Explanation: Two equal square rooms placed along the 4 m length each occupy half that length, so each square has side 4 m ÷ 2 = 2 m.
Correct answer: 2- A. 42%
- B. 62%
- C. 82%
- D. none of these
Explanation: Let the square's side be s units, so its area is s² square units. The new dimensions are 1.4s and 1.3s, giving area 1.4s × 1.3s = 1.82s²…
Correct answer: 82%- A. Rs.500
- B. Rs. 600
- C. Rs. 700
- D. Rs. 800
Explanation: The outer dimensions including the 2.5 m verandah on both sides are 25 m and 20 m, so the outer area is 500 m².
Correct answer: Rs. 700- A. 9:1
- B. 3:1
- C. 3:4
- D. 1:3
Explanation: The area ratio of squares equals the square of their side ratio, so a 9:1 area ratio gives side ratio √9:√1 = 3:1.
Correct answer: 3:1- A. 37 ½ %
- B. 60 %
- C. 75 %
- D. 120%
Explanation: When the length becomes 160% of its original value, the width must become 100/160 = 62.5% to preserve the same area.
Correct answer: 37 ½ %- A. 15
- B. 20
- C. 30
- D. 60
Explanation: Let the square's side be s cm. The rectangle's breadth is 3s/2 cm, so its area is 40 cm × 3s/2 cm = 60s cm², while the square's area is s²…
Correct answer: 20- A. 15m
- B. 4m
- C. 3m
- D. None of these
Explanation: Let the breadth be b m, so the length is 4b/3 m. From (4b/3) × b = 300 m², we get b² = 225 m² and b = 15 m, while the length is 20 m…
Correct answer: None of these