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 7 of 11
- A. 4/3 times its radius
- B. 2/3 times its radius
- C. Equal to it's radius
- D. Equal to it's diameter
Explanation: Equal volumes give pi x r^2 x h = 4/3 x pi x r^3, where r is the common radius.
Correct answer: 4/3 times its radius- A. 3
- B. 4
- C. 5
- D. 6
Explanation: Each sphere has radius 3 cm, so its volume is 4/3 x pi x 3^3 = 36pi cm3.
Correct answer: 5- A. 24.3 m
- B. 243 m
- C. 2430 m
- D. 24300 m
Explanation: The sphere radius is 9 cm, so its volume is 4/3 x pi x 9^3 = 972pi cm3.
Correct answer: 24300 m124. The radius of a wire is decreased to one -third if volume remains the same length will increase
- A. 1 Time
- B. 3 times
- C. 6 times
- D. 9 times
Explanation: For a wire, volume is cross-sectional area x length, so pi x r^2 x L remains constant.
Correct answer: 9 times- A. 8: 1
- B. 2√2 : 1
- C. 2 : 1
- D. None of these
Explanation: The volume of a cube is proportional to the cube of its edge. If the volume ratio is 8:1, the edge ratio is cube root of 8 : cube root of…
Correct answer: 2 : 1- A. 284 cm2
- B. 286 cm2
- C. 296 cm2
- D. 300 cm2
Explanation: The melted sheet has volume 27 cm x 8 cm x 1 cm = 216 cm3, so the cube edge is cube root of 216 cm3 = 6 cm.
Correct answer: 286 cm2- A. 1200000
- B. 1000000
- C. 9800000
- D. 7500000
Explanation: Convert the wooden box dimensions to centimetres: 8 m x 7 m x 6 m = 800 cm x 700 cm x 600 cm.
Correct answer: 1000000- A. 90, 85, 60
- B. 85, 75, 60
- C. 90, 75, 70
- D. 90, 75,60
Explanation: Let the dimensions be 6x cm, 5x cm and 4x cm. The total surface area is 2(6x x 5x + 5x x 4x + 4x x 6x) cm2 = 148x^2 cm2, so x^2 =…
Correct answer: 90, 75,60- A. 1300 m3
- B. 1331 m3
- C. 1452 m3
- D. 1542 m3
Explanation: For a cube, surface area is 6a^2, so 6a^2 = 726 m2 gives a^2 = 121 m2 and a = 11 m. Its volume is a^3 = 11^3 m3 = 1331 m3.
Correct answer: 1331 m3- A. 3:8
- B. 9:16
- C. 9:32
- D. 9:64
Explanation: The base perimeter is proportional to the radius, so the radii are in the ratio 3:4.
Correct answer: 9:32- A. 1:64
- B. 1:8
- C. 1:4
- D. 8:1
Explanation: Sphere surface area is proportional to r^2, so a surface-area ratio of 1:4 gives a radius ratio of 1:2.
Correct answer: 1:8- A. 3:4
- B. 9:16
- C. 1:8
- D. 4:3
Explanation: Sphere volume is proportional to the cube of its diameter. With diameters in the ratio 1:2, the volume ratio is 1^3:2^3 = 1:8.
Correct answer: 1:8- A. 1:2
- B. 1:4
- C. 2:1
- D. 4:1
Explanation: The surface area of a sphere is proportional to the square of its diameter.
Correct answer: 1:4- A. 1:2
- B. 1:4
- C. 1:8
- D. 2:1
Explanation: Cube volume is proportional to the cube of its side. Thus sides in the ratio 1:2 produce volumes in the ratio 1^3:2^3 = 1:8.
Correct answer: 1:8- A. 500
- B. 1000
- C. 900
- D. 600Computer Online Quiz
Explanation: Convert the small-box dimensions to metres: 60 cm = 0.6 m, 50 cm = 0.5 m and 40 cm = 0.4 m.
Correct answer: 1000- A. 24000
- B. 23000
- C. 22000
- D. 25000
Explanation: The wall volume is 25 m x 2 m x 0.75 m = 37.5 m3. Each brick has volume 20 cm x 10 cm x 7.5 cm = 1500 cm3 = 0.0015 m3, so the number of…
Correct answer: 25000- A. 100 cu.m
- B. 1000 cu.m
- C. 10000 cu.m
- D. 2000 cu.m
Explanation: The volume of a rectangular pond is length x width x depth = 20 m x 10 m x 5 m = 1000 m3.
Correct answer: 1000 cu.m- A. 100%
- B. 200%
- C. 300%
- D. 400%
Explanation: A cone's volume is V = 1/3 x pi x r2 x h, so with radius fixed, its volume is directly proportional to its height.
Correct answer: 100%- A. 1:3
- B. 3:1
- C. 1:2
- D. 2:1
Explanation: For the same radius r and height h, the cylinder volume is pi r2h, while the cone volume is 1/3 pi r2h.
Correct answer: 3:1- A. 8.66 m
- B. 5.196 m
- C. 6.928 m
- D. 7.264 m
Explanation: The longest rod in a cubical room is the space diagonal, not an edge or a face diagonal.
Correct answer: 6.928 m