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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- A. 10
- B. 8
- C. 9
- D. None of TheseInteractive math quizzes
Explanation: Since n((AUB)') = 10 and n(U) = 60, n(AUB) = 60 - 10 = 50. Using n(AUB) = n(A) + n(B) - n(A∩B), we get 50 = 35 + 24 - n(A∩B), so n(A∩B) =…
Correct answer: 9- A. 45434 square foot
- B. 34343 square foot
- C. 43572 square foot
- D. 43560 square foot
Explanation: The standard land-area conversion is 1 acre = 43,560 square feet. Therefore the correct value is 43,560 square foot, not 43,572 square…
Correct answer: 43560 square foot- A. 25 %
- B. 55%
- C. 40.5 %
- D. 56.25 %Quiz Mode Feature
Explanation: If the original side is s units, the new side is 1.25s units. Area changes by the square of the side factor, so the new area is (1.25)^2s²…
Correct answer: 56.25 %Quiz Mode Feature- A. 1 Hectometers
- B. 2 Hectometers
- C. 3 Hectometers
- D. 4 Hectometers
Explanation: One decameter equals 10 meters, so 10 decameters = 10 × 10 meters = 100 meters.
Correct answer: 1 Hectometers- A. 9 %
- B. 30 %
- C. 60 %
- D. 69 %Primary & Secondary Schooling (K-12)
Explanation: If the original side is s, the new side is 1.30s. The area changes from s² to (1.30s)² = 1.69s², so the increase is 1.69 − 1 = 0.69 = 69%.
Correct answer: 69 %Primary & Secondary Schooling (K-12)- A. 1200 m²
- B. 1500 m²
- C. 12000 m²
- D. 15000 m²
Explanation: A scale of 1:500 makes the actual length 30 cm × 500 = 15,000 cm = 150 m and the actual breadth 20 cm × 500 = 10,000 cm = 100 m.
Correct answer: 15000 m²- A. 54 cm
- B. 27 cm
- C. 12 cm
- D. 15 cm
Explanation: Let the length and breadth be 5k cm and 4k cm. Since the area is 180 cm², 5k × 4k = 20k² = 180, so k² = 9 and k = 3 cm; the sides are 15…
Correct answer: 54 cm- A. 1.4 m
- B. 2.8 m
- C. 14 m
- D. None of these
Explanation: Convert the capacity: 246.4 L = 0.2464 m³. Using V = πr²h, r² = 0.2464 m³ ÷ (4 m x 22/7) = 0.0196 m², so r = 0.14 m and diameter = 2 x…
Correct answer: None of these- A. 12 kg
- B. 60 kg
- C. 72 kg
- D. 96 kg
Explanation: The sinking displaces water with volume 3 m x 2 m x 0.01 m = 0.06 m3. Since floating equilibrium makes the displaced water's mass equal to…
Correct answer: 60 kg- A. the volume of the box
- B. twice the volume of the box
- C. the square of the volume of the box
- D. the cube root of the volume of the box
Explanation: If the box edges are a, b and c, the three adjacent face areas are ab, bc and ca.
Correct answer: the square of the volume of the box- A. 24 cm3
- B. 48 cm3
- C. 64 cm3
- D. 120 cm3
Explanation: Let the edges be x cm, 2x cm and 3x cm. The total surface area is 2(x x 2x + 2x x 3x + 3x x x) = 22x2 cm2, so 22x2 cm2 = 88 cm2 gives x =…
Correct answer: 48 cm3- A. 8
- B. 16
- C. 27
- D. 64
Explanation: A cube's space diagonal is a√3, where a is its edge. Thus a√3 cm = 4√3 cm gives a = 4 cm, and its volume is a3 = 4 cm x 4 cm x 4 cm = 64…
Correct answer: 64- A. 6
- B. 9
- C. 24
- D. 30
Explanation: To obtain the least number of equal cubes, use the largest cube edge that divides all three dimensions: gcd(6 cm, 9 cm, 12 cm) = 3 cm.
Correct answer: 24- A. 3m
- B. 5m
- C. 8.75m
- D. 10m
Explanation: If the path has width w metres inside the field, its area is 38 m × 32 m minus (38 − 2w) m × (32 − 2w) m.
Correct answer: 5m- A. 36cm
- B. 38cm
- C. 28cm
- D. 18cm
Explanation: For a rectangle, diagonal² = length² + breadth². Therefore breadth² = 10² square centimetres − 8² square centimetres = 100 square…
Correct answer: 28cm- A. 21 Sq.m
- B. 42 Sq.m
- C. 54 Sq.m
- D. 108 Sq.m
Explanation: The area of the four walls of a rectangular room equals its floor perimeter multiplied by height.
Correct answer: 54 Sq.m- A. 430
- B. 440
- C. 450
- D. 460
Explanation: Convert the sides to centimetres: 3.78 metres = 378 centimetres and 5.25 metres = 525 centimetres.
Correct answer: 450- A. 11m
- B. 13m
- C. 15m
- D. 17m
Explanation: Let the length and breadth be L metres and B metres. From the perimeter, 2(L + B) = 46 metres, so L + B = 23 metres; with LB = 120 square…
Correct answer: 17m- A. 25m
- B. 30m
- C. 44m
- D. None of these
Explanation: Let the breadth be b metres, so the length is 4.5b metres. The area equation is 4.5b² square metres = 200 square metres, giving b² = 200 ÷…
Correct answer: 30m- A. 5m
- B. 12m
- C. 13m
- D. 14.5m
Explanation: Let the shorter side be s metres, the longer side be l metres, and the diagonal be d metres.
Correct answer: 12mArea and Volume MCQs: common questions
Are these Area and Volume MCQs free?
Yes. All Area and Volume MCQs from Mathematics are free on TestUstad, with unlimited attempts and no account needed. Nothing on this page is a sample or a trial.
How many Area and Volume MCQs are on this page?
There are 204 Area and Volume MCQs in the Mathematics bank, shown 20 to a page with the correct answer and an explanation on each.
Does every Area and Volume MCQ have an explanation?
Yes. Each Area and Volume question shows the correct option and a written explanation of why it is correct, so a wrong answer teaches you something rather than just being marked wrong.
Can I take a timed Area and Volume test?
Yes. The practice button on this page starts a free Area and Volume test drawn from the Mathematics bank. It marks each answer instantly, gives you a score at the end, and can be retaken as many times as you like.