Question

If a cube has a surface area of 150 in?, what is its volume?

Answer 1

The surface area (A) of a cube is computed as follows:

$A=6\cdot a^2$

where a is the length of the cube edges

Substituting with A = 150 in², and solving for a:

$\begin{gathered} 150=6\cdot a^2 \\ \frac{150}{6}=a^2 \\ 25=a^2 \\ \sqrt[]{25}=a \\ 5\text{ in = }a \end{gathered}$

The volume (V) of a cube is calculated as follows:

$V=a^3$

Substituting with a = 5 in:

$\begin{gathered} V=5^3 \\ V=125in^3 \end{gathered}$