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zzz [600]
3 years ago
7

Can someone please help me with this question

Mathematics
1 answer:
Agata [3.3K]3 years ago
4 0

The volume of the styrofoam collar is approximately 1,960.35 in^{3} .

Step-by-step explanation:

Step 1:

The given styrofoam collar is a hollow cylinder. A hollow cylinder consists of an outer radius and an inner radius.

This given hollow cylinder has an outer radius of 8 inches and an inner radius of 5 inches. The height of the cylinder is 16 inches.

To calculate the volume of a hollow cylinder we subtract the volume of a cylinder constructed with the inner radius from the volume of a cylinder with the outer radius.

Step 2:

The volume of a cylinder, V = \pi r^{2} h.

For the outer cylinder, r = 8 inches and h=16 inches.

The volume of the outer cylinder, V_{1} = \pi (8^{2})(16) = 3,216.99.

For the inner cylinder, r = 5 inches and h=16 inches.

The volume of the inner cylinder, V_{2} = \pi (5^{2})(16) = 1,256.637.

Step 3:

The volume of the styrofoam collar = V_{1} -V_{2},

The volume of the styrofoam collar = 3,216.99-1,256.637 = 1,960.353.

Rounding this off, we get the volume of the styrofoam collar as 1,960.35 in^{3} .

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