The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing when the diameter is 60 mm

The volume is increasing at a rate of 33929.3 cubic millimeters per second.

Step-by-step explanation:

Volume of a sphere:

The volume of a sphere of radius r is given by:

In this question:

We have to derivate V and r implicitly in function of time, so:

The radius of a sphere is increasing at a rate of 3 mm/s.

This means that

How fast is the volume increasing when the diameter is 60 mm?

Radius is half the diameter, so . We have to find . So

The volume is increasing at a rate of 33929.3 cubic millimeters per second.

1. 22

2. 1

3. 7

4. 18

step-by-step explanation

e2020 got it right

1 + (6 / x - 1)

step-by-step explanation:

divide using polynomial division.