Question

The side of three cubes are in ratio 1:3:4 and their volume is 31556m^3 . Find the side of each cube.

Answer 1

Answer :

The side of each cube :- 7, 21 and 28 ( respectively ) .

Solution :

Let the common factor in their ratios be ' x '

Also, volume of cube = ( side )³

Now,

According to question :

$\sf (1x)^3 + (3x)^3 + (4x)^3 = 31556$

$\sf\implies 1x^3 + 27x^3 + 64x^3 = 31556$

$\sf\implies 92x^3 = 31556$

$\sf \implies x^3 = \dfrac{31556}{92}$

⇒$x = 3\sqrt{343}$

∴ x = 7

Now,

substitute the value of x in their sides.

• 1x = 1 × 7 = 7 m
• 3x = 3 × 7 = 21 m
• 4x = 4 × 7 = 28 m

$\rule{200}2$