## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.1

Question 1.

Which of the following numbers are not perfect cubes? Give reasons in support of your answer:

(i) 648

(ii) 729

(iii) 8640

(iv) 8000

Solution:

Question 2.

Show that each of the following numbers is a perfect cube. Also, find the number whose cube is the given number:

(i) 1728

(ii) 5832

(iii) 13824

(iv) 35937

Solution:

Question 3.

Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:

(i) 243

(ii) 3072

(iii) 11979

(iv) 19652

Solution:

Question 4.

Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube:

(i) 1536

(ii) 10985

(iii) 28672

(iv) 13718

Solution:

Question 5.

Rahul makes a cuboid of plasticine of sides 3 cm × 3 cm × 5 cm. How many such cuboids will he need to form a cube?

Solution:

Question 6.

Find the volume of a cubical box whose surface area is 486 cm^{2}.

Solution:

Question 7.

Which of the following are cubes of even natural numbers or odd natural numbers:

(i) 125

(ii) 512

(iii) 1000

(iv) 2197

(v) 4096

(vi) 6859

Solution:

Question 8.

Write the ones digit of the cube of each of the following numbers:

(i) 231

(ii) 358

(iii) 419

(iv) 725

(v) 854

(vi) 987

(vii) 752

(viii) 893

Solution:

Question 9.

Find the cubes of the following numbers:

(i) 13

(ii) \(3 \frac{1}{5}\)

(iii) \(-5 \frac{1}{7}\)

Solution: