Question

each side of a cube is doubled. in what ratio will the surface area increase?

Answer 1

total surface area of cube is 6 X side square then side is doubled so area becomes 24 a square then ratio is 1 by 4

Answer 2

The ratio of the surface areas of cube is 1 : 4.

Step-by-step explanation:

Let the side of the cube = a

To find, the ratio of the surface areas of cube = ?

We kow that,

The surface areas of cube $=6a^{2}$

The new side of the cube = 2a

The new surface areas of cube $=6(2a)^2$

$=6\times 4a^2$

$=24a^2$

∴ $\dfrac{The surface areas of cube}{The new surface areas of cube}=\dfrac{6a^2}{24a^2}$

$=\dfrac{1}{4}$

= 1 : 4

Hence, the ratio of the surface areas of cube is 1 : 4.