Question

two cubes have volumes in the ratio 27 216 what is the ratio of the area of the face of one cube to that of the other cube?​

Answer 1

The ratio of the area of the face of one cube to that of the other cube is

1: 4.

Step-by-step explanation:

Let side of first cube = $a_{1}$ and side of first cube = $a_{2}$

Given,

Two cubes have volumes in the ratio is 27:216.

We know that.

Volume of cube = $(Side)^{3}$

∴ Volume of first cube = $a_{1}^{3}$

⇒ [$a_{1^{3}= 27$

⇒$a_{1}^{3}= 3^{2}$

∴ $a_{1} =3$

Area of first cube = $6a_{1} ^{2}$

=$= 6\times 9=54$

Also, Volume of first cube = $a_{2}^{3}$

⇒[$a_{2}^{3}=6^{2}$

∴ $a_{2} =6$

Area of first cube = $6a_{2} ^{2}$

$= 6\times 36=216$

∴ The ratio of the area of the face of one cube to that of the other cube

= 54 : 216 =$\dfrac{54}{216}$= 1:4.