Question

The dimensions of a rectangular block , in form of a cuboid is in the ratio of 5:4:3. If the volume of the block is equal to the volume of a cube of length 28 cm, find the length of the longest side of the cuboid, giving your answer correct to one decimal place.

Answer 1

Therefore the length of the longest side of the cuboid is =36 cm.

Step-by-step explanation:

Given, the dimension of a rectangular block in from of cuboid is in the ratio 5:4:3. The volume of the block is equal to the volume of cube of length 28 cm.

The volume of the cube is = 28³ cm³ =21952 cm³

Let the length , breadth and height of the cuboid be 5x , 4x and 3x respectively.

The volume of the cuboid is =(5x.4x.3x)cm³ = 60x³ cm³

According to the problem,

60x³ = 21952

$\Rightarrow x^3=\frac{21952}{60}$

⇒x=7.2

Therefore the length of the longest side of the cuboid is = (7.2×5)cm=36 cm.