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, l3 = 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, 60x3 = 480
Or, x3 = 480/60
Or, x3 = 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, 125x3 – 64x3 = 61
Or, 61x3 = 61
Or, x3 = 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 83 = 512
∴ cube of smaller num = 512 – 387
= 125
= 53
∴ Smaller num = 5