Question

Two cubes have their volume in the ratio 1:27. Find the ratio of their surface area

Answer 1

consider the image for solution

Answer 2

Answer:

The ratio of their surface area is 1:9.

Step-by-step explanation:

It is given that the two cubes have their volume in the ratio 1:27.

Let the side length of first and second cubes are a₁ and a₂ respectively.

Volume of cone is

$V=a^3$

Where, a is side length of cube.

The ratio of volume of cubes is 1:27.

$\frac{V_1}{V_2}=\frac{1}{27}$

$\frac{a_1^3}{a_2^3}=\frac{1}{27}$

Taking cube roots both the sides.

$\frac{a_1}{a_2}=\frac{1}{3}$

The ratio of side lengths is 1:3.

The ratio of area is

$\frac{a_1^2}{a_2^2}= \frac{1^2}{3^2}$

$\frac{a_1^2}{a_2^2}= \frac{1}{9}$

Therefore the ratio of their surface area is 1:9.