**ML Aggarwal CBSE Solutions Class 8 Math 4th Chapter Cubes and Cube Roots Exercise 4.2**

**(7)** Vol of cubic box = 21952 m

∴ let one side of b ox = l m

We know that,

l x l x l = 21952

Or, l^{3} = 21952

Or, l = √21952

= √28x28x28

= l = 28 m

**(8)** Ratio of three number = 3 : 4 : 5

∴ their product = 480

Let, the common factor = x

According to question

3x X 4x X 5x = 480

Or, 60x^{3} = 480

Or, x^{3} = 480/60

Or, x^{3} = 8

Or, x = √8 = √2x2x2

Or, x = 2

∴ 1st num = 3x = 3 x 2 = 6

2nd num = 4x = 4 x 2 = 8

3rd num = 5x = 5 x 2 = 10

∴ Number are 6, 8 , 10

**(9)** 1st num : 2nd num = 4:5

let, common factor = x

∴ 1st num 4x

2nd num = 9x

According to the question –

(5x)^{3} – (4x)^{3} = 61

Or, 125x^{3} – 64x^{3} = 61

Or, 61x^{3} = 61

Or, x^{3} = 61/61

Or, x = √1

Or, x = 1

Therefore, 1st number is = 4 x 1 = 4

2nd number 5 x 1 = 5

**(10)** Different of two perfect cube = 387

∴ greater num = 8

∴ cube of 8^{3} = 512

∴ cube of smaller num = 512 – 387

= 125

= 5^{3}

∴ Smaller num = 5