The base radius of a cone is expanding at the rate of 1in/min while its height is shrinking at the rate of 3in/min. How fast is the volume of this cone changing at the moment when the base radius is 30 in and the height is 40in?

The volume of the cone is shrinking at the rate cubic inches / min.

Step-by-step explanation:

Formula:

Given that,

The base of a cone is expanding at the rate of 1 in / min while it height is shrinking at the rate  3 in/ min.

i.e  

         and

   [ since height is shirking]

The volume of a cone is

Differentiating with respect to t

Now putting    and  

To find the rate of changing volume at the moment when base radius is 30 in and the height is 40 in, we need to put r= 30 in and h=40 in.

                      cubic inches / min

The volume of the cone is shrinking at the rate cubic inches / min.

4038

step-by-step explanation:

pleaze mark brainliest!

step-by-step explanation: