Question

A cube has an edge of 2 feet. The edge is increasing at the rate of 5 feet per minute. Express the volume of the cube as a function of m, the number of minutes elapsed.

Answer 1

`V(m) = (2 + 5m)^3`

Explanation:

Given

Solid Shape = Cube

Edge = 2 feet

Increment = 5 feet per minute

Required

Determine volume as a function of minute

From the question, we have that the edge of the cube increases in a minute by 5 feet

This implies that,the edge will increase by 5m feet in m minutes;

Hence,

`New\ Edge = 2 + 5m`

Volume of a cube is calculated as thus;

`Volume = Edge^3`

Substitute 2 + 5m for Edge

`Volume = (2 + 5m)^3`

Represent Volume as a function of m

`V(m) = (2 + 5m)^3`