Question

as sand leaks out of a hole in a container, it forms a pile in the shape of a right circular cone whose height is always the same as its radius. The height of the pile is increasing at a rate of 6 in/min. Find an expression for the rate of change of the volume of the sand in terms of the height of the pile.
b. Find the rate of the change of the volume of the sand when the height of the pile is 10 inches.

Answer 1

To start you off.............

Volume of a cone, V = (1/3)(pi)(r^2)(h)
where r= radius and h = height.

In this problem, we are told that the radius = height, so we will replave r with h.

so V = (1/3)(pi)(h^2)(h)
V = (1/3) (pi)(h^3)

we want to find dV/dt when dh/dt = 6.

You will differentiate both sides of the equation with respect to time, so you'll have dV/dt = .............

To find dV/dt...you'll substitute what is given.