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

Option B: 67.02 cubic inches

Given that:

The diagram consists of two parts:

• First a cone on the top with 12 inches height and 4 inches diameter.

• Second a semi sphere with diameter of 4 inches.

Calculations:

The amount of foams that can be stuffed with foam is total volume of both the containers.

Volume of the given cone of 12 inches height and 4 inches diameter can be given as:

$\dfrac{1}{3} \times \pi \times 2^2 \times 12\\= 50.265 \: \rm inch ^3$

Volume of the semi sphere of 4 inches diameter can be given as:

$\dfrac{2}{3} \pi \times 2^3\\= 16.755 \: \rm inch^3$

Thus total volume is 50.265 + 16.755 = 67.02 cubic inches.

Thus option B : 67.02 cubic inches is the needed volume.

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