Question

Aimee packs ice cream into a cone She puts a perfect hemisphere of ice cream on top of the cone that has a volume of 4 inches ^3. The diameter of the ice cream cone is equal to its height. What is the total volume of ice cream in and on top of the cone? Use the relationship between the the formulas for the volumes of cones and spheres to help solves this problem. Show your work and explain the reasoning

Answer 1

8 in³

Explanation:

Volume of a sphere is:

V = ⁴/₃ πr³

Volume of a hemisphere is half of that:

V = ⅔ πr³

Volume of a cone is:

V = ⅓ πr²h

The height of the cone is equal to the diameter, so h = 2r.

V = ⅓ πr²(2r)

V = ⅔ πr³

The hemisphere and cone have the same radius, so they have the same volume. So the total volume is 4 in³ + 4 in³ = 8 in³.