Related rates problem?
a pint of ice cream is eaten causing the height of the ice cream in the cylindrical container to drop at a rate of 1 inch/min. the pint is 4 inches in diameter and 5.5 inches tall. how fast, in cubic inches per minute, is the volume of ice cream being eaten?
a pint of ice cream is eaten causing the height of the ice cream in the cylindrical container to drop at a rate of 1 inch/min. the pint is 4 inches in diameter and 5.5 inches tall. how fast, in cubic inches per minute, is the volume of ice cream being eaten?
1 Answer
Explanation:
First I want it to made apparently clear that we are finding the rate of volume or
We know from geometry that the volume of a cylinder is found by using the formula
Secondly, we know
Thirdly, our
We now find a derivative of our Volume using a Product Rule with respect to time, so:
If we think about the cylinder, our radius isn't changing. That would mean the shape of the cylinder would have to change. Meaning
so, by plugging in our varriable:
with units