Question

Two cubes have their volumes in the ratio 1 : 27. What is the ratio of their surface areas?

Answer 1

The rate of the value of cubes = 1:27

 `(a_1^3)/(a_2^2) = 1/27`

`a_1 /a_2 = 1/3` …… (i)

Now,

The ratio of their surface area

`s_1 : s_2 = 6a_1^2 :6a_2^2`

 `s_1/s_2 =(6a_1^2)/(6^2)`

      `=(a_1/a_2)^2`

`s_1 /s_2 = 1/9`

Hence, `s_1 : s_2 = 1 : 9`