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Answer:
The volume of the cone is changing at a rate of approximately 8670.796 cubic inches per second.
Step-by-step explanation:
Geometrically speaking, the volume of the right circular cone (), in cubic inches, is defined by the following formula:
(1)
Where:
- Radius, in inches.
- Height, in inches.
Then, we derive an expression for the rate of change of the volume (), in cubic inches per second, by derivatives:
(2)
Where:
- Rate of change of the radius, in inches per second.
- Rate of change of the height, in inches per second.
If we know that ,
,
and
, then the rate of change of the volume is:
The volume of the cone is changing at a rate of approximately 8670.796 cubic inches per second.