# 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.

## Answer and Explanation:

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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from Glencoe Pre-Algebra: Online Textbook Help

Chapter 8 / Lesson 7