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.

This ICSE Class 8 Mathematics practice quiz has 50 multiple-choice questions on Cubes and Cube Roots, and 50 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. If a cube has a volume of 1728 cubic centimeters, what is the length of one of its edges?

   1. 10 cm
   2. 12 cm
   3. 14 cm
   4. 16 cm
   Show answer

   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).

2. The volume of a cubical box is 343 cubic units. What is the length of the longest diagonal of the box?

   1. 7√3 units
   2. 7√2 units
   3. 7 units
   4. 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.

3. The edge of a cube is 'a' cm. If 'a' is increased by 10%, what is the percentage increase in its volume?

   1. 10%
   2. 21%
   3. 33.1%
   4. 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%.

4. If the volume of a cube is 1728 cubic inches, what is the length of the diagonal of the cube?

   1. 12 inches
   2. 12√2 inches
   3. 12√3 inches
   4. 144 inches
   Show answer

   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.

5. If a cube has a total surface area of 216 square cm, what is its volume?

   1. 125 cm³
   2. 216 cm³
   3. 243 cm³
   4. 343 cm³
   Show answer

   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.

More questions in this quiz

Answers and explanations are in the full quiz.

1. The cube root of a number is 9. What is the number?
2. If the edge of a cube is 3.5 cm, what is its volume?
3. Which of the following is the cube root of 0.000064?
4. If a cuboid has dimensions 2 cm, 3 cm, and 4 cm, what is the volume of the largest cube that can be cut from it?
5. The volume of a cube is 1331 cubic meters. What is the length of its side?
6. Which of the following numbers, when cubed, will result in a number ending in 7?
7. If a cube has a surface area of 294 square centimeters, what is the length of its edge?
8. What is the cube root of 32768?
9. If a cubical box has a volume of 512 cubic inches, what is the total surface area of the box?
10. Which of the following numbers is NOT a perfect cube?
11. If the side of a cube is doubled, by what factor does its volume increase?
12. Find the smallest number that must be subtracted from 1000 to make it a perfect cube.
13. What is the cube root of 0.000729?
14. If a cube has a volume of V and its edge length is 'a', what is the relationship between V and 'a'?
15. What is the value of 9³ - 8³?
16. The volume of a cube is 0.125 cubic meters. What is the length of its side?
17. If a cube has a volume of 1000 cubic feet, what is its total surface area?
18. What is the smallest perfect cube that is divisible by both 4 and 6?
19. Which of the following is the cube root of 1/64?
20. The volume of a cube is 27 cubic cm. What is the length of the diagonal of one of its faces?
21. What is the smallest number by which 108 must be multiplied to make it a perfect cube?
22. If the volume of a cube is 216 cubic cm, what is the sum of the lengths of all its edges?
23. What is the cube root of -216?
24. If the surface area of a cube is 150 sq units, what is its volume?
25. Which of the following numbers, when cubed, will result in a number ending in 8?
26. What is the smallest number by which 432 must be multiplied to make it a perfect cube?
27. What is the cube root of 1000000?
28. What is the cube of -5?
29. The sum of the digits of a two-digit number is 9. If the digits are reversed, the new number is 9/4 times the original number. What is the original number?
30. What is the sum of the cubes of the first five natural numbers?
31. If the volume of a cube is 4096 cubic feet, what is the length of the side?
32. If a cube has a side length of 10 cm, what is its volume?
33. What is the cube root of 1728/343?
34. What is the smallest positive integer whose cube root is a rational number?
35. If the side of a cube is reduced by 20%, by what percentage does its volume decrease?
36. What is the cube root of -0.000027?
37. The volume of a cube is 3375 cubic cm. What is the length of the edge?
38. If the side of a cube is increased by 100%, what is the percentage increase in its volume?
39. What is the cube root of 0.512?
40. If the volume of a cube is 27 cubic cm, what is the length of the longest diagonal of the cube?
41. The volume of a cube is 64 cubic feet. What is the surface area of the cube?
42. What is the cube root of 2197?
43. If a cube has a volume of 729 cubic inches, what is the sum of the lengths of all its edges?
44. Which of the following numbers, when cubed, will result in a number ending in 5?
45. The volume of a cubical box is 1000 cubic cm. What is the length of the diagonal of one of its faces?

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