A waffle cone has a height of 6in with a radius at the top being 1 inch. A spherical scoop of ice cream is placed on top of the cone and melts into the cone. At a particular instant of time, the radius of the ice cream is 3/2 inch and is decreasing by 1/100 in/min. At this same time, the height of the melted ice cream in the cone is 2 inches. How is the height of the melted ice cream in the cone changing?
Some quick facts from geometry
Volume of sphere: S = 4/3 pi R^3
Volume of cone: C = 1/3 pi r^2 h
where R is the radius of the sphere of ice cream,
pi is the number pi,
r is the radius of the cone at the level of the ice cream,
and h is the height of the ice cream in the cone.
The real trick of setting up the problem is to think about where the ice cream is going. Assuming no ice cream drips down the side, then ice cream leaving the sphere
goes into the cone.
So, the rate of decrease of ...
This shows how to find the rate of change of height of ice cream melting in a cone.