Question

Two cubes have volumes in the ratio $1:64$.

The ratio of the area of a face of first cube to that of the other is

• A. $1:4$
• B. $1:8$
• C. $1:16$
• D. $1:32$

Answer 1

The correct option is C

$1:16$

Finding the ratios of the area of the cubes:

Volume of Cube $=a^3$

Let the side of first cube is $a$

the side of second cube is $b$

The ratio of their volume equal to

$$\begin{gathered} \frac{a^3}{b^3}=\frac{1}{64} \\ \frac{a}{b}=\frac{1}{4} \end{gathered}$$

Thus, the ratio of the areas are:

$\begin{array}{rcl}{\left(\frac{a}{b}\right)}^2& =& {\left(\frac{1}{4}\right)}^2\\ & =& \frac{1}{16}\end{array}$

Therefore the ratio of their areas is equal to $1:16$