Use 3.14... Thank you so much

Question

Midvale theater is considering using cylinders to serve popcorn.The measurements are radius 3 in and height 7. Part A: The manager of the theater wants to sell the popcorn in a cone with a diameter of 7 in.What does the height of the cone need to be in order to hold the same amount of popcorn as the cylinder?

Answer 1

The height needs to be about 15.5 in.

Answer 2

If you look at the formula for volume of a cylinder: V = Bh where B is pi times r² because of circular base; i.e.,

Volume of cylinder is pi(r²)h

 

The formula for volume of a right circular cone is V = (1/3)(pi)r²h.

 

This shows that, for a circular base or radius r and height h, the volume of a cone is one third of that of a cylinder of the same height.

 

So the cone needs to be 3 times as tall as the cylinder.

 

P.S. 3.14 is NOT pi--it's a very poor approximation. To 4 decimal places, pi is 3.1416, but that's just a better approximation.