Chapter 12, Problem 15PT

To determine

To calculate:To find the volume of cube if the dimensions of cube are doubled

Answer to Problem 15PT

New volume of cube is $64$ cubic inches

Explanation of Solution

Given information:A cube has a volume of 8 cubic inches

Formula Used:

Volume of cube of side $a$ is calculated as

  $V=a^3$

When side of cube is doubled, new side $a^{\prime }=2a$

Thus, new volume is

  $\begin{array}{l}{V}^{\prime }={\left(2a\right)}^3\\ V^{\prime }=8a^3\end{array}$

Calculation:

Given that a cube has a volume of 8 cubic inches

Also, dimensions of cube are doubled

Thus, new volume of cube is calculated as

  $V^{\prime }=8a^3$

Substituting the values,

  $\begin{array}{l}{V}^{\prime }=8\left(a^3\right)\\ V^{\prime }=8\left(8\right)\\ V^{\prime }=64i{n}^3\end{array}$

Conclusion:

Hence, new volume of cube is $64$ cubic inches