Chapter 4.4, Problem 51WE

To determine

To find out the volumes of two cubes shown.

Answer to Problem 51WE

The volume of cubes are $8x^3$ and $64x^3$

Explanation of Solution

Given:

The given cubes are-

Calculation:

Finding the volume of smaller cube-

  $\begin{array}{l}=2x\times 2x\times 2x\\ =8x^3\end{array}$

Finding the volume of larger cube-

  $\begin{array}{l}=4x\times 4x\times 4x\\ =64x^3\end{array}$

To determine

To find out which cube has larger volume.

Answer to Problem 51WE

The larger cube has larger volume.

Explanation of Solution

Given:

The given cubes are-

Calculation:

Finding the volume of smaller cube-

  $\begin{array}{l}=2x\times 2x\times 2x\\ =8x^3\end{array}$

Finding the volume of larger cube-

  $\begin{array}{l}=4x\times 4x\times 4x\\ =64x^3\end{array}$

Clearly, the larger cube has larger volume.

To determine

To find out how many times bigger cube has larger volume.

Answer to Problem 51WE

  $8$ Times.

Explanation of Solution

Given:

The given cubes are-

Calculation:

The number of times bigger cube has larger volume is-

  $\begin{array}{l}=\frac{64x^3}{8x^3}\\ =8\end{array}$