Question

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

Answer 1

Answer:

Ratio of their curved surface areas 9:16

Step-by-step explanation:

Assume that the tins are cube in shape

Let a and b be the length of the sides of given cubes

Given:

$V_1:V_2=27:64$

$\implies\:\frac{V_1}{V_2}=\frac{27}{64}$

$\implies\:\frac{a^3}{b^3}=\frac{3^3}{4^3}$

$\implies\:(\frac{a}{b})^3=(\frac{3}{4})^3$

$\implies\:\frac{a}{b}=\frac{3}{4}$

Now

$\text{Ratio of their curved surface areas}$

$=4a^2:4b^2$

$=a^2:b^2$

$=3^2:4^2$

$=9:16$