Free Geometry MCQs with Answers
222 Geometry MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Geometry examines points, lines, angles, triangles, polygons, circles, and three-dimensional figures through properties, theorems, and formulas. Questions connect angle relationships and triangle rules with calculations of perimeter, area, surface area, and volume, so area must not be confused with the space enclosed by a solid.
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222 questions · page 7 of 12
- 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