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 pie ~ 3.14.
r=5in
R=8in
h=23in
To find the volume of the collar, we need to find the difference in volume between the larger and smaller cones that make up the collar.
The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height.
First, let's calculate the volume of the larger cone:
V_larger = (1/3)πR^2h
= (1/3)π(8^2)(23)
= (1/3)π(64)(23)
= (1/3)(3.14)(64)(23)
≈ 1508.64 in^3
Now let's calculate the volume of the smaller cone:
V_smaller = (1/3)πr^2h
= (1/3)π(5^2)(23)
= (1/3)π(25)(23)
= (1/3)(3.14)(25)(23)
≈ 1199.17 in^3
Finally, we can find the volume of the collar by subtracting the volume of the smaller cone from the volume of the larger cone:
V_collar = V_larger - V_smaller
= 1508.64 - 1199.17
≈ 309.47 in^3
Therefore, the volume of the Styrofoam collar is approximately 309.47 cubic inches.