Question

Two tins are geometrically similar. If the ratio of their volume is 27:64 find the ratio of their curved surface area.

Answer 1

9 : 16

Explanation:

Given 2 similar figures with linear ratio = a : b, then

area ratio = a² : b² and

volume ratio = a³ : b³

Here the volume ratio = 27 : 64, hence

linear ratio =
`\sqrt[3]{27}` :
`\sqrt[3]{64}` = 3 : 4

Hence area ratio = 3² : 4² = 9 : 16