Question

If the sides of two cubes are in the ratio 4:1 the ratio of their volumes is?

Answer 1

let, the length of sides of the cubes are 4x and x
the ratio of their volumes is----
$( {4x}^{3} ) \div ( {x}^{3} ) \\ = 64 \div 1$
=64:1

Answer 2

The ratio of volume is 64 : 1

Step-by-step explanation:

If the length of a side is a units, breadth of side is b, height of the side is h, and the volume of a cube is abh units.

A cube is an object which is having 6 faces with the shape of a square.

Since, it’s a cube of equal length, breadth, and height. So, all sides are equal.

$\text{Volume of cube} = a^3\ \text{units}$

Given that ratio of the sides of two cubes is 4 : 1

i.e.,  

Let C1 be the cube with side a1 and C2 be the cube with side a2

Given that sides of two cubes are in the ratio 4 : 1

$\Rightarrow a 1 : a 2=4 : 1$

Let V1 be the Volume of cube C1, V2 be the volume of cube C2.

Consider ratio of their volumes,

$V 1 : V 2=a 1^{3} : a 2^{3}$

$\Rightarrow 4 \times 4 \times 4 : 1 \times 1 \times 1=64 : 1$