The radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.3 in/s. At what rate is the volume of the cone changing when the radius is 110 in. and the height is 151 in.

The volume is changing at a rate given by:

Step-by-step explanation:

Let's recall the formula for the volume of acone, since it is the rate of the cone changing what we need to

Volume of cone =

where B is the area of the base (a circle of radius R) which equals =

and where H stands for the cone's height.

We apply the derivative over time operator () on both sides of the volume equation, making sure that we apply the rule for the derivative of a product:

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step-by-step explanation: