A collar of Styrofoam is made to insulate a pipe. Find its volume . The large R is to the outer rim. The small radius r is to the edge of the insulation. Use 3.14 for pi. r = 5 in. R = 6 in. h = 19 in. Round to two decimal places. It says to subtract volume of the inner cylinder from the volume of the outer cylinder. Round answer two decimal places.
subscribe to callmecarson on yt
To find the volume of the collar of Styrofoam, you need to subtract the volume of the inner cylinder from the volume of the outer cylinder.
Volume of the outer cylinder:
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. In this case, the radius of the outer cylinder is R = 6 in and the height is h = 19 in.
V_outer = π(R^2)h
V_outer = 3.14(6^2)(19)
V_outer = 3.14 * 36 *19
V_outer = 2149.04 in^3
Volume of the inner cylinder:
The radius of the inner cylinder is r = 5 in and the height is the same as before, h = 19 in.
V_inner = π(r^2)h
V_inner = 3.14(5^2)(19)
V_inner = 3.14 * 25 * 19
V_inner = 1492.5 in^3
Finally, to find the volume of the collar, subtract the volume of the inner cylinder from the volume of the outer cylinder.
Volume of the collar = V_outer - V_inner
Volume of the collar = 2149.04 - 1492.5
Volume of the collar = 656.54 in^3
Therefore, the volume of the collar of Styrofoam is approximately 656.54 cubic inches, rounded to two decimal places.
To find the volume of the collar of Styrofoam, you need to subtract the volume of the inner cylinder from the volume of the outer cylinder. Here's how you can calculate it:
Step 1: Calculate the volume of the outer cylinder:
The formula to calculate the volume of a cylinder is given by V = π * r^2 * h, where V is the volume, π is approximately 3.14, r is the radius, and h is the height (or thickness) of the cylinder.
Given:
Outer radius, R = 6 in
Height, h = 19 in
Using the formula, the volume of the outer cylinder is:
V_outer = π * R^2 * h
= 3.14 * 6^2 * 19
≈ 2150.52 cubic inches
Step 2: Calculate the volume of the inner cylinder:
Given:
Inner radius, r = 5 in
Height, h = 19 in
Using the same formula, the volume of the inner cylinder is:
V_inner = π * r^2 * h
= 3.14 * 5^2 * 19
≈ 1501.1 cubic inches
Step 3: Calculate the volume of the collar:
To find the volume of the collar, we subtract the volume of the inner cylinder from the volume of the outer cylinder:
V_collar = V_outer - V_inner
= 2150.52 - 1501.1
≈ 649.42 cubic inches
Therefore, the volume of the collar of Styrofoam is approximately 649.42 cubic inches.