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?© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/math/calculus-and-analysis/a-related-rates-calculus-problem-in-regards-to-a-cone-1n9
...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 ...