# A related rates calculus problem in regards to a cone.

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?

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...e of the sphere equals the rate of increase of volume inside the cone.

Write things using derivatives:

S' = - C'

where the ' means d/dt.

One problem is that the cone has both a radius r and a height h.

We can relate those two by using similar triangles.

If you look at a cone in a cross-section, you get an upside down isosceles triangle. By drawing a vertical line down the middle you make a right angle triangle with the top side being 1 (the radius of the cone) and the vertical edge being 6 ...