Cubes and Cube Roots Quiz - ICSE Class 8 Mathematics
Free practice quiz: Cubes and Cube Roots (ICSE Class 8 Mathematics). 50 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
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If a cube has a volume of 1728 cubic centimeters, what is the length of one of its edges?
- 10 cm
- 12 cm
- 14 cm
- 16 cm
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Answer: B. 12 cm
The volume of a cube is given by the formula V = s³, where 's' is the length of an edge. To find the edge length, we need to calculate the cube root of the volume. The cube root of 1728 is 12 (since 12 x 12 x 12 = 1728).
The volume of a cubical box is 343 cubic units. What is the length of the longest diagonal of the box?
- 7√3 units
- 7√2 units
- 7 units
- 21 units
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Answer: A. 7√3 units
First, find the edge length of the cube. V = s³. 343 = s³. The cube root of 343 is 7 (since 7³ = 343). So, the edge length (s) is 7 units. The longest diagonal of a cube (space diagonal) is given by the formula d = s√3. Substituting s = 7, we get d = 7√3 units.
The edge of a cube is 'a' cm. If 'a' is increased by 10%, what is the percentage increase in its volume?
- 10%
- 21%
- 33.1%
- 72.9%
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Answer: C. 33.1%
Let the original edge length be 'a'. The original volume is V₁ = a³. If the edge length is increased by 10%, the new edge length becomes a + 0.10a = 1.10a. The new volume is V₂ = (1.10a)³ = (1.10)³ * a³ = 1.331a³. The increase in volume is V₂ - V₁ = 1.331a³ - a³ = 0.331a³. The percentage increase in volume is ((V₂ - V₁) / V₁) * 100% = (0.331a³ / a³) * 100% = 0.331 * 100% = 33.1%.
If the volume of a cube is 1728 cubic inches, what is the length of the diagonal of the cube?
- 12 inches
- 12√2 inches
- 12√3 inches
- 144 inches
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Answer: C. 12√3 inches
First, find the edge length of the cube. V = s³. 1728 = s³. We need to find the cube root of 1728. 10³ = 1000, 12³ = 12 x 12 x 12 = 144 x 12 = 1728. So, the edge length (s) is 12 inches. The longest diagonal (space diagonal) of a cube is given by d = s√3. Substituting s = 12 inches, we get d = 12√3 inches.
If a cube has a total surface area of 216 square cm, what is its volume?
- 125 cm³
- 216 cm³
- 243 cm³
- 343 cm³
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Answer: B. 216 cm³
The surface area of a cube is SA = 6s². We are given SA = 216 sq cm. So, 6s² = 216. Divide both sides by 6: s² = 216 / 6 = 36. Take the square root of both sides: s = √36 = 6 cm. Now, calculate the volume: V = s³ = 6³ = 6 x 6 x 6 = 216 cubic cm.