SOLUTION: Larry's ice cream is installing a giant ice cone above the shop. The plans for the ice cream cone, which is constructed by connecting a hemisphere to a cone. The cone is 6 ft and

Algebra ->  Volume -> SOLUTION: Larry's ice cream is installing a giant ice cone above the shop. The plans for the ice cream cone, which is constructed by connecting a hemisphere to a cone. The cone is 6 ft and      Log On


   

Question 258330: Larry's ice cream is installing a giant ice cone above the shop. The plans for the ice cream cone, which is constructed by connecting a hemisphere to a cone. The cone is 6 ft and the entire ice cream cone is 9 ft. What is the volume of the ice cream cone
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
volume of a sphere is equal to 4/3 * pi * r^3

volume of a cone is equal to 1/3 * pi * r^2 * h

the cone is 6 feet high and the entire ice cream cone is 9 feet.

this means that the radius of the sphere is 3 feet.

this is also the radius of the base of the cone.

volume of the sphere is 4/3 * pi * 3^3 = 4/3 * pi * 27 = 4 * pi * 9 = 36 * pi.

take half of that to get the top half of the sphere only and you get the volume of the icream on top of the cone is equal to 18 * pi.

volume of the cone is 1/3 * pi * r^2 * h

r = 3 and h = 6

volume of the cone is 1/3 * pi * (3)^2 * 6 = 18 * pi.

volume of the ice cream cone is equal to 18 * pi + 18 * pi = 36 * pi.

36 * pi = 113.0973355 cubic feet.

click on the following link to see a picture of the cone.

http://theo.x10hosting.com/problems/258330.jpg