## anonymous 3 years ago The volume. V cm^3, of a cone of height h is (pi)h^3/12. If h increases at a constant rate of 0.2cm/s and the initial height is 2cm, express V in interms of t and find the rate of change of V at time t.

1. myininaya

So we have $V(x)=\frac{\pi }{12} (h(x))^3$ We will let x represent the variable time for now.

2. myininaya

Find derivative of both sides.

3. myininaya

With respect to x

4. myininaya

Both V and h are functions of time this implies that both V and h are functions of x

5. myininaya

So derivative of V is V' and derivative of h is h'

6. myininaya

So tell me what does V' equal?