The area of the base B and the height h of a pyramid are related to the pyramid's volume V by the formula V =1/3Bh. How is dV/dt related to dh/dt if B is constant?
I chose C, but my teacher said try again? The available answers are:
A) dV/dt =B/3(dh/dt)
B) dV/dt = B dh/dt
C) dV/dt =1/3 (dh/dt)
D) dV/dt =dh/dt

Would it just be D?

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 V =1/3Bh. How is dV/dt related to dh/dt if B is constant? 
I chose C, but my teacher said try again? The available answers are:
A) dV/dt =B/3(dh/dt)
B) dV/dt = B dh/dt
C) dV/dt =1/3 (dh/dt)
D) dV/dt =dh/dt  

Would it just be D?

ybarrap · Answer

V = (1/3) B * h
(dV/dt) = (1/3) B * (dh/dt ) + (1/3)*(dB/dt) * h , by chain rule
            = (1/3) B * (dh/dt)