Question

A collar of Styrofoam is made to insulate a pipe.

Find its volume. The large radius R is to the outer rim. The small radius r is to the edge of the insulation. Use r ~ 3.14.
r = 3 in.
R = 5 in.
h = 16 in.

Answer 1

Answer: 1256

Explanation:

Assuming the object in question is a right circular cylinder with insulation on the top and bottom, we can use the formula for the volume of such a cylinder to find its volume.

The formula for the volume of a right circular cylinder is:

V = πr^2h

where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is a mathematical constant that is approximately equal to 3.14.

However, since the cylinder in question has insulation, we need to adjust the radius of the base accordingly. Since the small radius r is to the edge of the insulation, the radius of the base of the cylinder with insulation is r + h = 3 + 16 = 19 inches.

The volume of the cylinder is then:

V = πR^2h

where R is the large radius to the outer rim. Substituting the given values, we get:

V = π(5 in)^2(16 in)

V = π(25 in^2)(16 in)

V = 400π in^3

Therefore, the volume of the cylinder with insulation is 400π cubic inches.