All the edges of a cube are expanding at a rate of 4 in. per second. How fast is the volume changing when each edge is 10 in. long

Given:

All the edges of a cube are expanding at a rate of 4 in. per second.

To find:

The rate of change in volume when each edge is 10 in. long.

Solution:

Let a be the edge of the cube.

According to the question, we get

We know that, volume of a cube is

Differentiate with respect to t.

Putting the given values, we get

Therefore, the rate of change in volume 1200 cubic inches per second.

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