Question

A hollow toy, with the dimensions shown in the figure, is to be stuffed with rigid foam. What is the maximum amount of foam that can be stuffed into the toy? Round your answer to two decimal places. Assume that both parts are stuffed and the foam does not expand or contract.
A) 52.46 cubic inches

B) 67.02 cubic inches

C) 83.78 cubic inches

D) 112.15 cubic inches

Answer 1

I saw the figure that should have accompanied this problem. It looks like an ice cream cone. A cone and a half sphere.

The height of the cone is 12 inches, its diameter is 4 inches.
The half sphere has a diameter of 4 inches.

Volume of a cone = π r² h/3 = 3.14 * (2in)² * 12in/3 = 3.14 * 4in² * 4in = 50.24in³

Volume of a sphere = 4/3 π r³ = 4/3 * 3.14 * (2in)³ = 4/3 * 3.14 * 8in³ = 33.49in³
Volume of the half sphere = 33.49in³/2 = 16.75in³

Total volume = 50.24in³ + 16.75in³ = 66.99 in³  or B.) 67.02 CUBIC INCHES