Answer:
[tex]\frac{dV}{dt}=\frac{B}{3}*\frac{dH}{dt}[/tex]
Step-by-step explanation:
The volume of a pyramid is given by:
[tex]V=\frac{1}{3}Bh[/tex]
The derivate for the volume expression as a function of height is:
[tex]\frac{dV}{dh}=\frac{1}{3}B\\[/tex]
We can write that dt/dt = 1. Therefore, the relationship between dV/dt and dh/dt, if B is constant, is given by:
[tex]\frac{dV}{dh}=\frac{1}{3}B*1\\\frac{dV}{dh}=\frac{1}{3}B*\frac{dt}{dt}\\\frac{dV}{dt}=\frac{B}{3}*\frac{dH}{dt}[/tex]
