A hypothetical cube grows so that the length of its sides are increasing at a rate of 2 m/min. How fast is the volume of the cube increasing when the sides are 8m each?

In a min the volume increased by 296m^3

Step-by-step explanation:

Volume of cube = v^3

At 8m = V = 8*8*8 = 512

Since it's growing at 2m/min

The previous volume A min ago would have been

8m - 2m = 6m

V = 6*6*6 = 216

So in a minute, the volume had gone from 216 to 512

The speed = 512 - 216 = 296

So it's volume increased by 296 in a min.

Just for future clarification.

(2 min ago the volume would have been.

8m - (2*2) m = 4

V 2min ago = 4*4*4 = 64.

At 2mins ago the volume changed by 216 - 64 = 152.

So this is what the volume looked like Each minute

0, 8, 64, 216, 512, 1000.)