Answer:
The radius is increasing at a rate of 62832 cubic millimeters per second when the diameter is of 100 mm.
Step-by-step explanation:
Volume of a sphere:
The volume of a sphere of radius r is given by:
How fast is the volume increasing:
To find this, we have to differentiate the variables of the problem, which are V and r, implicitly in function of time. So
The radius of a sphere is increasing at a rate of 2 mm/s.
This means that
How fast is the volume increasing (in mm3/s) when the diameter is 100 mm?
Radius is half the diameter, so
Then
The radius is increasing at a rate of 62832 cubic millimeters per second when the diameter is of 100 mm.