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steposvetlana [31]
3 years ago
5

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. lo

ng
Mathematics
1 answer:
Greeley [361]3 years ago
5 0

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

\dfrac{da}{dt}=4\text{ in./sec}

a=10\text{ in.}

We know that, volume of a cube is

V=a^3

Differentiate with respect to t.

\dfrac{dV}{dt}=\dfrac{d}{dt}a^3

\dfrac{dV}{dt}=(3a^2)\times \dfrac{da}{dt}

Putting the given values, we get

\dfrac{dV}{dt}=(3(10)^2)\times 4

\dfrac{dV}{dt}=3(100)\times 4

\dfrac{dV}{dt}=300\times 4

\dfrac{dV}{dt}=1200\text{ in}^3\text{/sec}

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

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