Question

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.

Answer 1

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

Answer 2

Find derivative of both sides.

Answer 3

With respect to x

Answer 4

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

Answer 5

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

Answer 6

So tell me what does V' equal?