The volume (V) of a cone of radius r and height A ts given by the formula V = 1/3 pi r^2 h To use...

The volume (V) of a cone of radius r and height A ts given by the formula V = 1/3 pi r^2 h To use the formula to calculate the volume of a cone, you need to be given the radius and height of the cone. 1. Find the following derivatives for V = 1/3 pi r^2 h 2. The derivative dV/dh is a formula for the change In volume with respect to a change in __ A) What information about the cone Is needed in order to calculate a value for dV/dh? dH 3. The derivative dV/dr is a formula for the charge in volume with respect to a change in __, A) What information about the cone must be given In order to calculate a value for dV/dr? Neither of the above situations are very realistic. It is more reasonable to think of all three variables changing with respect to time! The volume (V) changes as the radius r and height h of the cone changes. V(t) = 1/3 pi r^2 h where BOTH r and h are functions of time or V (t) = 1/3 pi (r(t))^2 middot h(t) 4. Find the derivative for the volume function with respect to time. This will require the use of the product rule as well as implicit differentiation (the chain rule) since both r and h are functions of t, as in r(t) and h(t) dV/dt = __ 5. What information must be given In order to calculate a value for dV/dt? List everything that would be needed. 6. Suppose the height h of the cone is always twice the radius r, determine the volume for such a cone and find the change in volume with respect to time. (Note: Since h = 2r you can simplify the volume formula. V(t) = and dV/dt = __ 7. What information must be given in order to calculate a value for dV/dt now?