Question

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

Answer 1

`(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)`