Question

A cube has an edge of 3 feet. The edge is increasing at the rate of 2 feet per minute. Express the volume of the cube as a function of m, the number of minutes elapsed.

Answer 1

The volume of a cube is defined as

`\begin{gathered} V_{\text{cube}}=s^3 \\ \text{where} \\ s\text{ is the edge of the cube} \end{gathered}`

Then we can write it as a function of m as

`\begin{gathered} V(m)=s^3_{} \\ \\ \text{Since }s\text{ increases at a rate of }2\text{ feet per minute then} \\ s=3+2m \end{gathered}`

We can now rewrite it as

`\begin{gathered} V(m)=s^3 \\ \text{substitute }s=3+2m \\ \\ V(m)=(3+2m)^3 \end{gathered}`