The cube of 4 is 64 and 125 is a perfect cube, so recognising cubes and cube roots carries this Grade 8 sheet. Later answers include a cube root of 8, the cube root of −27 as −3, and a value of 500 in the key.
Key Takeaways
4³ = 64 (Q1).
125 is a perfect cube (Q2).
The key records ∛512 = 8 and ∛(−27) = −3.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.What is the cube of 4?
(a) 8(b) 16(c) 64(d) 12
2.Which of the following is a perfect cube?
(a) 81(b) 100(c) 125(d) 200
3.The cube root of 512 is:
(a) 6(b) 7(c) 8(d) 9
4.What is the value of ∛(−27)?
(a) 3(b) −3(c) 9(d) −9
5.How many digits are in the cube of a 2-digit number?
(a) 4(b) 5(c) 6(d) Can be 4 or 5
6.Which number is not a perfect cube?
(a) 216(b) 343(c) 500(d) 729
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Find the smallest number by which 72 must be multiplied to make it a perfect cube.
8.Evaluate: ∛(64 × 125).
9.Find the cube root of 3375 by prime factorisation.
10.Is 392 a perfect cube? If not, find the smallest number by which it must be divided to get a perfect cube.
11.Find the cube of (−12).
12.Find the volume of a cube whose side is 11 cm.
13.Evaluate: ∛(216/343).
14.The cube of a number is 9,261. Find the number.
Section C: Word Problems (3 Marks Each)
Apply the concepts to solve real-life problems.
15.A cubical water tank can hold 1331 litres of water. Find the side length of the tank (1 litre = 1000 cm³).
16.Three numbers are in the ratio 1:2:3. The sum of their cubes is 7,776. Find the numbers.
17.How many cuboidal boxes of dimensions 2 cm × 2 cm × 2 cm can be packed into a cubical box of side 12 cm?
18.The volume of a cubical block is 343 cm³. Find the length of its side.
19.A company ships items in cubical boxes of side 0.5 m. Find the volume of one box in cubic centimetres.
20.If ∛(x) = 15, find the value of x.
Answer Key
1. c) 64
2. c) 125
3. c) 8
4. b) −3
5. d) Can be 4 or 5
6. c) 500
7. Refer to solution guide.
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End of Worksheet
People Also Ask
What is the cube of 4?
64, option (c) in this worksheet (Q1).
Which of these is a perfect cube?
125, option (c) in this worksheet (Q2).
What is the value of ∛(−27)?
−3, from the answer key on this page.
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