Question

The volume of a right circular cone is given by

V=(1/3)3.14r^2*h, where r is the radius and h is the height.
Find dV/dt if r=4, h=5, dr/dt=6, and dh/dt=-3

Please try to show as much work as possible

Answer 1

Since both r and h are changing with time, you need to use the partial derivative relationship

dV/dt = dV/dh*dh/dt + dV/dr*dr/dt
where dV/dh and dV/dr are partial derivatives. They should use a "lazy d" symbol that I cannot type here.

When computing a partial derivative with respect to one variable, assume that the other variable(s) is/are constant.

Try the steps yourself; further help will be provide if you need it.