Question

the dimension of a cuboid box are in the ratio of 5:4:2 . If its volume is 1080 cm3 , find the dimension of the box.​

Answer 1

Answer:

let the ratio be x

5x 4x 2x

volume = side *side*side

5x*4x*2x=1080

40x^3=1080

x^3=1080/40

x^3=27

x=3

5x=15

4x=20

2x=6

Answer 2

Given ratio = 5:4:2

Let the sides be 5x, 4x & 2x.

Volume of cuboid = l × b × h

$1080 = 5x \times 4x \times 2x \\ \\ 1080 = 40 {x}^{3} \\ \\ \frac{1080}{40} = {x}^{3} \\ \\ 27 = {x}^{3} \\ \\ x = \sqrt[3]{27} \\ \\ x = 3 \: cm$

So the dimensions are:-

5x = 5(3) = 15 cm

4x = 4(3) = 12 cm

2x = 2(3) = 6 cm

Answer:- Dimension = 15 × 12 × 6 cm

Hope it helps.