Question

Can someone please help me with this question

Answer 1

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 $in^{3} .$