Question

The volumes of the two cubes are in the ratio 64:27. Find the ratio of their surface areas.

• A. $9:16$
• B. $16:25$
• C. $16:9$
• D. $4:3$

Answer 1

The correct option is C $16:9$

Given: Ratio of volumes = 64:27.
$\Rightarrow \frac{Volumeofcubeofsidea}{Volumeofcubeofsideb}=\frac{a^3}{b^3}=\frac{64}{27}$
$\Rightarrow \frac{a}{b}=\frac{4}{3}$
Now, ratio of surface area of cubes$=\frac{Surfaceareaofcubeofsidea}{Surfaceareaofcubeofsideb}=\frac{6a^2}{6b^2}=\frac{a^2}{b^2}=\frac{4^2}{3^2}(\because \frac{a}{b}=\frac{4}{3})=\frac{16}{9}$
Therefore, the required ratio is $16:9$.