Question

Two cubes have their volumes in the ratio $1:27$ find the ratio of their surface

Answer 1

Finding the ratio of the surface area:

Given:

The ratio of volume of two cubes $=1:27$

Solution:

Volume of first cube$=a^3$

Volume of second cube$=b^3$

now ,

$\begin{array}{rcl}\frac{a^3}{b^3}& =& \frac{1}{27}\\ \frac{a}{b}& =& \sqrt[3]{\frac{1}{27}}\\ \frac{a}{b}& =& \frac{1}{3}\\ 3a& =& b\end{array}$

Ratio of surface area

$\begin{array}{rcl}& =& \frac{6a^2}{6b^2}\\ & =& \frac{a^2}{b^2}\\ & =& \frac{a^2}{{\left(3a\right)}^2}\\ & =& \frac{a^2}{9a^2}\\ & =& \frac{1}{9}\end{array}$

Therefore the ratio of their areas is $1:9$