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 9 of 12
- A. 30 π cc
- B. 45 π cc
- C. 150 π cc
- D. 180 π cc
Explanation: The diameter is 6 cm, so the radius is 3 cm. The cylinder's volume is πr²h = π × (3 cm)² × 5 cm = 45π cm³.
Correct answer: 45 π cc- A. 18 πr2 sq units
- B. 3 πr2 sq units
- C. 12 πr2 sq units
- D. 6 πr2 sq units
Explanation: The curved surface area of a cylinder is 2πrh. With r = 2r units and h = 3r units, it becomes 2π × 2r × 3r = 12πr² square units.
Correct answer: 12 πr2 sq units- A. 2.66 cm
- B. 2.5 cm
- C. 3 cm
- D. 3.5 cm
Explanation: For spheres, volume is proportional to the cube of the diameter, so 3³ cm³ = (1.5 cm)³ + (2 cm)³ + d³.
Correct answer: 2.5 cm- A. 100π
- B. 7π
- C. 60π
- D. 50π
Explanation: Eight equal balls have one-eighth of the original sphere's volume, so each ball has radius 10 cm ÷ 2 = 5 cm because volume scales with the…
Correct answer: 100π- A. 1:4
- B. 1:16
- C. 1:8
- D. 1:64
Explanation: Sphere area is proportional to r², so an area ratio of 1:4 gives a radius ratio of 1:2.
Correct answer: 1:8166. The volumes of two cubes are in the ratio 27: 125, what shall be the ratio of their surface areas?
- A. 6:25
- B. 3:5
- C. 9:25
- D. 16:25
Explanation: Cube volume is proportional to the cube of its edge, so a volume ratio of 27:125 gives an edge ratio of 3:5.
Correct answer: 9:25- A. 15840 m
- B. 16840 m
- C. 15820 m
- D. 15640 m
Explanation: The square's side is √69696 m² = 264 m. Its perimeter is 4 × 264 m = 1056 m, and 15 rounds require 15 × 1056 m = 15840 m of wire.
Correct answer: 15840 m- A. 8 cm
- B. 12 cm
- C. 14 cm
- D. 10 cm
Explanation: The total volume of the melted cubes is 6³ cm³ + 8³ cm³ + 10³ cm³ = 216 cm³ + 512 cm³ + 1000 cm³ = 1728 cm³.
Correct answer: 12 cm- A. 3:1
- B. 8:1
- C. 9:1
- D. 12:1
Explanation: The total surface area of a cube is 6a², so surface area varies as the square of its side.
Correct answer: 9:1- A. 5 cm
- B. 19 cm
- C. 13 cm
- D. 144 cm
Explanation: The diagonal of a cuboid is √(l² + b² + h²). Thus it is √[(3 cm)² + (4 cm)² + (12 cm)²] = √(9 cm² + 16 cm² + 144 cm²) = √169 cm² = 13 cm.
Correct answer: 13 cm- A. 120 cm2
- B. 148 cm2
- C. 74 cm2
- D. 15 cm2
Explanation: The surface area of a cuboid is 2(lw + lh + wh), so 2[(4 cm x 5 cm) + (4 cm x 6 cm) + (5 cm x 6 cm)] = 2(20 + 24 + 30) cm2 = 148 cm2.
Correct answer: 148 cm2- A. 3 dm
- B. 4 dm
- C. 5 dm
- D. 6 dm
Explanation: The combined volume is 3^3 dm3 + 4^3 dm3 + 5^3 dm3 = 27 dm3 + 64 dm3 + 125 dm3 = 216 dm3.
Correct answer: 6 dm- A. 50
- B. 64
- C. 216
- D. 125
Explanation: A metre cube has side 10 dm. Along each dimension, 10 dm ÷ 2 dm = 5 cubes fit, so the total number is 5 x 5 x 5 = 125 cubes.
Correct answer: 125- A. 864 cm2
- B. 648 cm2
- C. 486 cm2
- D. 468 cm2
Explanation: For a cube, side^3 = 1728 cm3, so the side is 12 cm because 12 x 12 x 12 = 1728 cm3.
Correct answer: 864 cm2- A. 8 cc
- B. 16 cc
- C. 32 cc
- D. 64 cc
Explanation: The surface area is 6a^2, so 6a^2 = 24 cm2 gives a^2 = 4 cm2 and a = 2 cm. Therefore the volume is a^3 = (2 cm)^3 = 8 cm3.
Correct answer: 8 cc- A. 6a2 cm2
- B. 8a2 cm2
- C. 12a2 cm2
- D. 24a2 cm2
Explanation: A cube has surface area 6a^2 when its edge is a. With edge 2a cm, the surface area is 6(2a cm)^2 = 6 x 4a^2 cm2 = 24a^2 cm2.
Correct answer: 24a2 cm2- A. 2h
- B. 4h
- C. 2h/3
- D. 3h/2
Explanation: Let the common base radius be r and the cylinder height be H. The cone volume is (1/3)πr^2h, while the cylinder volume is πr^2H; since…
Correct answer: 2h/3- A. 100 %
- B. 200 %
- C. 700 %
- D. 800 %
Explanation: Sphere volume is proportional to the cube of its radius. Doubling the radius multiplies the volume by 2^3 = 8, so the increase is 8 - 1 =…
Correct answer: 700 %- A. 3 : 7
- B. 7 : 3
- C. 6 : 7
- D. 7 : 6Downloading Interactive Party Trivia Games
Explanation: Using curved surface area 2πrh = 264 m2 and volume πr^2h = 924 m3, division gives r/2 = 924 m3 ÷ 264 m2 = 3.5 m, so r = 7 m.
Correct answer: 7 : 3- A. 90 cm
- B. 1 dm
- C. 1 m
- D. 1.1 cm
Explanation: A cistern is normally understood to be open at the top. Its internal length and width are 3.3 m - 0.1 m = 3.2 m and 2.6 m - 0.1 m = 2.5 m…
Correct answer: 1 dm