If a cube has an edge of 2 feet. The edge is increasing at the rate of 6 feet per minute. How would i express the volume of the

Question

16 days ago

8

cube as a function of m, the number of minutes elapsed. V(m)= ??

1 answer:

PIT_PIT [12.4K] · Answer 1 · 2026-04-03T12:55:55+03:00

Answer:

v(m) = 8 + 48m+ 180m² +216m³

Step-by-step explanation:

First, lets express the edge of the cube as a function of time in minutes.

Initially, the edge measures 2 feet

Then as time passes, it increases at a rate of 6 feet per minute, meaning there will be a 6 feet increase for every minute that passes.

Let x represent the edge length

X = 2 + 6(m)

Here, m signifies the elapsed minutes.

The volume is defined as the cube of the edge length = edge³

but edge = x

So, V(m) = x³

Replacing x with (2+6m), we have V(m) = (2+6m)³

Thus, v(m) simplifies to 8 + 48m + 180m² + 216m³