Question

The value of x equals the number of cubic units in a box that is 4 units high, 4 units deep, and 4 units wide. Which equation can be used to determine the value of x?Math item stem image3x=644x=64x−−√=4x−−√3=4

Answer 1

The value of x equals the number of cubic units in a box that is 4 units high, 4 units deep, and 4 units wide.

Recall that the volume of a cube is given by

`V=l\cdot w\cdot h`

Where l is the length, w is the width, and h is the height of the cube.

We are given that all three sides are 4 units.

So, the volume is

`\begin{gathered} V=4\cdot4\cdot4\; \\ V=64\; \; cubic\; \text{units} \end{gathered}`

x must be equal to this volume

`x=64`

Take cube root on both sides of the equation

`\begin{gathered} \sqrt[3]{x}=\sqrt[3]{64} \\ \sqrt[3]{x}=\sqrt[3]{4^3} \\ \sqrt[3]{x}=4 \end{gathered}`

Therefore, the correct equation is the last option.

`\sqrt[3]{x}=4`