A collar of Styrofoam is made to insulate a pipe. Find its volume The large radius is to the outer rim. The small radius r is to the edge of the insulation. Use π for 3.14. r = 3 in R = 5 in h = 18 in. Round 2 decimal places
To find the volume of the collar, we first need to understand the shape of the collar. Based on the given information, we can assume that the collar consists of a larger cylinder with a smaller cylinder cut out from the center.
To find the volume, we need to calculate the volume of the larger cylinder and subtract the volume of the smaller cylinder.
1. Calculate the volume of the larger cylinder:
Volume_larger_cylinder = π * R^2 * h
= 3.14 * 5^2 * 18
2. Calculate the volume of the smaller cylinder:
First, we need to find the radius of the smaller cylinder by subtracting the given small radius from the large radius:
r_small = R - r
= 5 - 3
= 2 in
Volume_smaller_cylinder = π * r_small^2 * h
= 3.14 * 2^2 * 18
3. Subtract the volume of the smaller cylinder from the volume of the larger cylinder to get the volume of the collar:
Volume_collar = Volume_larger_cylinder - Volume_smaller_cylinder
Calculating the values:
Volume_larger_cylinder = 3.14 * 5^2 * 18
= 3.14 * 25 * 18
= 1413.0 in^3 (rounded to 2 decimal places)
Volume_smaller_cylinder = 3.14 * 2^2 * 18
= 3.14 * 4 * 18
= 226.08 in^3 (rounded to 2 decimal places)
Volume_collar = 1413.0 - 226.08
= 1186.92 in^3 (rounded to 2 decimal places)
Therefore, the volume of the Styrofoam collar is approximately 1186.92 cubic inches.
To find the volume of the Styrofoam collar, we need to subtract the volume of the inner cylinder (with radius r and height h) from the volume of the outer cylinder (with radius R and height h).
The volume of a cylinder can be calculated using the formula V = π * r^2 * h, where π is approximately 3.14.
First, let's calculate the volume of the outer cylinder:
V_outer = π * R^2 * h
Substituting the given values:
V_outer = 3.14 * 5^2 * 18
V_outer = 3.14 * 25 * 18
V_outer = 1413
Now, let's calculate the volume of the inner cylinder:
V_inner = π * r^2 * h
Substituting the given values:
V_inner = 3.14 * 3^2 * 18
V_inner = 3.14 * 9 * 18
V_inner = 508.68
Finally, the volume of the Styrofoam collar is given by:
Volume = V_outer - V_inner
Volume = 1413 - 508.68
Volume = 904.32
Therefore, the volume of the Styrofoam collar is approximately 904.32 cubic inches when rounded to 2 decimal places.