Wafer cone height

Question

The wafer cone shown is to hold 10 in^3 of ice cream when filled to the bottom. The diameter of the cone is 2 inches and the top of the ice cream has a shape of a hemisphere. Find the height h of the cone. (round two decimal places)

Answer 1

The volume of the hemisphere is (2/3)*π*r³.

Since the diameter of the cone was given as 2 inches, the radius is half of this, or 1 inch.

So the volume if this hemisphere is (2/3)*π inches³.

The volume of the cone is (h/3)*π*h*r².

So the volume of the cone is (h/3)*π inches².

So, h = [ 10 - (2/3)*π ] / ( π / 3 ) = 7.55 inches, rounded to 2 decimal places.