State whether the statements are true (T) or false (F).

For an integer a, a³ is always greater than a².

By taking three different, values of n verify the truth of the following statements:

(i) If n is even, then n³ is also even.

(ii) If n is odd, then n³ is also odd.

(ii) If n leaves remainder 1 when divided by 3, then n³ also leaves 1 as remainder when divided by 3.

(iv) If a natural number n is of the form 3p+2 then n³ also a number of the same type.

Which of the following numbers are not perfect cubes?

(i) 64

(ii) 216

(iii) 243

(iv) 1728

Find the cubes of the following numbers by column method:

(i) 35

(ii) 56

(iii) 72

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

31, 109, 388, 4276, 5922, 77774, 44447, 125125125

Which of the following are cubes of odd natural numbers?

125, 343, 1728, 4096, 32768, 6859

Find the volume of a cube whose surface area is 384m².

Choose the correct answer:

Write the cubes 5 natural numbers of which are multiples of 7 and verity the following:

“The cube of a multiple of 7 is a multiple of 7³.

Write the cubes 5 natural numbers of the from 3n+2(i.e.5,8,11….) and verify the following:

“The cube of a natural number of the form 3n+2 is a natural number of the same form i. e. when it is dividend by 3 the remainder is 2’

By what least number should 324 be multiplied to get a perfect cube?