Chapter 12.5, Problem 16PSB

To determine

To calculate: The volume of cube whose total surface area is $150i{n}^2$ .

Answer to Problem 16PSB

The volume of cube is $125i{n}^3$ .

Explanation of Solution

Given information:

Total surface area of cube = $150i{n}^2$ .

Formula used:

Volume of cube $=s^3$

s = side of cube.

Area of cube $=s^2$

s = side of cube.

Calculation:

  

In cube there are six faces.

Area of cube = 6 $\times$ area of one face.

  $150=6s^2$

  $\begin{array}{l}{s}^2=\frac{150}{6}\\ s^2=25\\ s=\sqrt{25}\\ s=5\end{array}$

Volume of cube:

  $\begin{array}{l}V=s^3\\ V={\left(5\right)}^3\\ V=125i{n}^3\end{array}$