Aimee packs ice cream into an ice cream cone. She then puts a perfect hemisphere of ice cream on top of the cone that has a volume of 4 in.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 formulas for the volumes of cones and spheres to help solve this problem. Show your work and explain your reasoning.

Answer 1

given: volume of cone = 4
height of cone = 2r
volume of cone = (1/3)π r^2 (2r) = 2/3 π r^3 = 4
π r^3 = 6

total volume = (1/2)(4/3)πr^3 + (1/3)π(r^2)(2r)
= (2/3) π r^3 + (2/3)π r^3
= (4/3)(6) = 8 in^3

Answer 2

Bot, can you be more clear in the process?