# A cube's surface area increases at the rate of 72 in^2/sec . At what rate is the cube's volume...

## Question:

A cube's surface area increases at the rate of 72 {eq}in^2/sec {/eq}. At what rate is the cube's volume changing when the edge length is x = 3 in.

## Rate of Change:

Let us first write the formula for the surface area of the cube and then differentiate it with respect to t. Then we will plug-in the values given in the problem to get the rate of change of area of cube.

To find the rate of change of the side we will proceed as

Let us first write the surface area of the cube which is

{eq}S=6a^{2} {/eq}

Now...

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