A tank is shaped like an upside-down square pyramid, with a base with sides that are 4 meters in length and a height of 12meters. If water is being pumped into the pyramid at a rate of 2/3  m3 /sec, at what rate is the height of the water increasing when the water is 2 meters deep? (The volume of a pyramid with height h and base area B is given by V=1/3 Bh.)Enter a fraction and do not include units.

Question
Asked Mar 16, 2019
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A tank is shaped like an upside-down square pyramid, with a base with sides that are 4 meters in length and a height of 12meters. If water is being pumped into the pyramid at a rate of 2/3  m3 /sec, at what rate is the height of the water increasing when the water is 2 meters deep? (The volume of a pyramid with height h and base area B is given by V=1/3 Bh.)

Enter a fraction and do not include units.

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Expert Answer

Step 1

We have to find rate of change of  height of pyramid.

Information is given below:

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Step 2

We will use following rules to find derivative.

Rules are given below:

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Step 3

Now with the help of above rules we will differentiate volume equation ,it will give realation between  dV/dt and dh/...

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Calculus

Derivative

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