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The area of the base B and the height h of a pyramid are related to the pyramid's volume V by the formula How is dV/dt related to dh/dt if B is constant

User Kee
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1 Answer

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Answer:


(dV)/(dt)=(B)/(3)*(dH)/(dt)

Explanation:

The volume of a pyramid is given by:


V=(1)/(3)Bh

The derivate for the volume expression as a function of height is:


(dV)/(dh)=(1)/(3)B\\

We can write that dt/dt = 1. Therefore, the relationship between dV/dt and dh/dt, if B is constant, is given by:


(dV)/(dh)=(1)/(3)B*1\\(dV)/(dh)=(1)/(3)B*(dt)/(dt)\\(dV)/(dt)=(B)/(3)*(dH)/(dt)

User Michael L
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