The radius of a cone is increasing at a constant rate of 8 feet per second. The volume remains a constant 56 cubic feet. At the instant when the radius of the cone is 3 feet, what is the rate of change of the height? The volume of a cone can be found with the equation V = farh. Round your answer to three decimal places.

Explanation:

The volume of a cone, V = 1/3πr^2h

Where r is the radius, and h is the height of the cone.

Given:

Volume is constant at 56 cubic feet.

Radius of cone increases at a constant rate of 8 feet per second.

The radius of the cone is 3 feet.

When radius is 3 feet

Where h is in feets.

Since the volume is constant so  

The rate of change of radius is  

The minus indicates that the rate of change of height is decreasing.