To find the volume of the Styrofoam collar, we first need to find the volumes of the two separate cylinders (one with radius R and height h, and one with radius r and height h) and then subtract the smaller cylinder from the larger one.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
For the larger cylinder with radius R and height h:
V1 = πR^2h
V1 = 3.14 * 6^2 * 24
V1 = 3.14 * 36 * 24
V1 = 2713.28 cubic inches
For the smaller cylinder with radius r and height h:
V2 = πr^2h
V2 = 3.14 * 3^2 * 24
V2 = 3.14 * 9 * 24
V2 = 678.24 cubic inches
The volume of the Styrofoam collar can be found by subtracting the volume of the smaller cylinder from the volume of the larger cylinder:
V_styrofoam = V1 - V2
V_styrofoam = 2713.28 - 678.24
V_styrofoam = 2035.04 cubic inches
Therefore, the volume of the Styrofoam collar is 2035.04 cubic inches.
Question content area top Part 1 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 pi almost equals 3.14 . r = 3 in. R = 6 in. h = 24 in.
9 answers
thats wrong
I apologize for the mistake. Let's correct this.
The volume of the Styrofoam collar can be calculated by finding the volume of the larger cylinder with radius R and height h, and then subtracting the volume of the smaller cylinder with radius r and height h. The volume of a cylinder is given by the formula V = πr^2h.
For the larger cylinder with radius R = 6 in and height h = 24 in:
V1 = π * R^2 * h
V1 = 3.14 * 6^2 * 24
V1 = 3.14 * 36 * 24
V1 = 2714.56 cubic inches
For the smaller cylinder with radius r = 3 in and height h = 24 in:
V2 = π * r^2 * h
V2 = 3.14 * 3^2 * 24
V2 = 3.14 * 9 * 24
V2 = 678.24 cubic inches
The volume of the Styrofoam collar is the difference between V1 and V2:
V_styrofoam = V1 - V2
V_styrofoam = 2714.56 - 678.24
V_styrofoam = 2036.32 cubic inches
Therefore, the volume of the Styrofoam collar is 2036.32 cubic inches. Thank you for pointing out the error.
The volume of the Styrofoam collar can be calculated by finding the volume of the larger cylinder with radius R and height h, and then subtracting the volume of the smaller cylinder with radius r and height h. The volume of a cylinder is given by the formula V = πr^2h.
For the larger cylinder with radius R = 6 in and height h = 24 in:
V1 = π * R^2 * h
V1 = 3.14 * 6^2 * 24
V1 = 3.14 * 36 * 24
V1 = 2714.56 cubic inches
For the smaller cylinder with radius r = 3 in and height h = 24 in:
V2 = π * r^2 * h
V2 = 3.14 * 3^2 * 24
V2 = 3.14 * 9 * 24
V2 = 678.24 cubic inches
The volume of the Styrofoam collar is the difference between V1 and V2:
V_styrofoam = V1 - V2
V_styrofoam = 2714.56 - 678.24
V_styrofoam = 2036.32 cubic inches
Therefore, the volume of the Styrofoam collar is 2036.32 cubic inches. Thank you for pointing out the error.
thats still wrong its 2034.72
I apologize for the oversight. Let's correct this calculation.
Given:
r = 3 in
R = 6 in
h = 24 in
π ≈ 3.14
Volume of the larger cylinder (V1):
V1 = πR^2h
V1 = 3.14 * 6^2 * 24
V1 = 3.14 * 36 * 24
V1 = 2716.16 cubic inches
Volume of the smaller cylinder (V2):
V2 = πr^2h
V2 = 3.14 * 3^2 * 24
V2 = 3.14 * 9 * 24
V2 = 678.24 cubic inches
Volume of the Styrofoam collar:
V_styrofoam = V1 - V2
V_styrofoam = 2716.16 - 678.24
V_styrofoam = 2037.92 cubic inches
Therefore, the correct volume of the Styrofoam collar is 2037.92 cubic inches. Thank you for your patience, and I apologize for the previous errors.
Given:
r = 3 in
R = 6 in
h = 24 in
π ≈ 3.14
Volume of the larger cylinder (V1):
V1 = πR^2h
V1 = 3.14 * 6^2 * 24
V1 = 3.14 * 36 * 24
V1 = 2716.16 cubic inches
Volume of the smaller cylinder (V2):
V2 = πr^2h
V2 = 3.14 * 3^2 * 24
V2 = 3.14 * 9 * 24
V2 = 678.24 cubic inches
Volume of the Styrofoam collar:
V_styrofoam = V1 - V2
V_styrofoam = 2716.16 - 678.24
V_styrofoam = 2037.92 cubic inches
Therefore, the correct volume of the Styrofoam collar is 2037.92 cubic inches. Thank you for your patience, and I apologize for the previous errors.
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 pi almost equals 3.14 . r = 5 in. R = 6 in. h = 19 in.
Given:
r = 5 in
R = 6 in
h = 19 in
π ≈ 3.14
To find the volume of the Styrofoam collar, we need to calculate the volume of the larger cylinder (with radius R and height h) and subtract the volume of the smaller cylinder (with radius r and height h).
Volume of the larger cylinder (V1):
V1 = πR^2h
V1 = 3.14 * 6^2 * 19
V1 = 3.14 * 36 * 19
V1 = 2145.84 cubic inches
Volume of the smaller cylinder (V2):
V2 = πr^2h
V2 = 3.14 * 5^2 * 19
V2 = 3.14 * 25 * 19
V2 = 1483.5 cubic inches
Volume of the Styrofoam collar:
V_styrofoam = V1 - V2
V_styrofoam = 2145.84 - 1483.5
V_styrofoam = 662.34 cubic inches
Therefore, the volume of the Styrofoam collar is 662.34 cubic inches.
r = 5 in
R = 6 in
h = 19 in
π ≈ 3.14
To find the volume of the Styrofoam collar, we need to calculate the volume of the larger cylinder (with radius R and height h) and subtract the volume of the smaller cylinder (with radius r and height h).
Volume of the larger cylinder (V1):
V1 = πR^2h
V1 = 3.14 * 6^2 * 19
V1 = 3.14 * 36 * 19
V1 = 2145.84 cubic inches
Volume of the smaller cylinder (V2):
V2 = πr^2h
V2 = 3.14 * 5^2 * 19
V2 = 3.14 * 25 * 19
V2 = 1483.5 cubic inches
Volume of the Styrofoam collar:
V_styrofoam = V1 - V2
V_styrofoam = 2145.84 - 1483.5
V_styrofoam = 662.34 cubic inches
Therefore, the volume of the Styrofoam collar is 662.34 cubic inches.
wrong
I apologize for the mistake. Let's re-calculate the volume of the Styrofoam collar with the correct values.
Given:
r = 5 in
R = 6 in
h = 19 in
π ≈ 3.14
Volume of the larger cylinder (V1):
V1 = πR^2h
V1 = 3.14 * 6^2 * 19
V1 = 3.14 * 36 * 19
V1 = 2145.84 cubic inches
Volume of the smaller cylinder (V2):
V2 = πr^2h
V2 = 3.14 * 5^2 * 19
V2 = 3.14 * 25 * 19
V2 = 4715 cubic inches
Volume of the Styrofoam collar:
V_styrofoam = V1 - V2
V_styrofoam = 2145.84 - 4715
V_styrofoam = -2569.16 cubic inches
Upon re-evaluation, it appears that there was an error in the calculation. The volume of a collar cannot be negative. Let's correct the calculation.
The correct formula to find the volume of the Styrofoam collar should involve the difference in volumes as before, but the calculation was not accurate. Let's re-calculate accurately:
V_styrofoam = V1 - V2
V_styrofoam = 2145.84 - 4715
V_styrofoam = -2569.16 cubic inches
Therefore, the volume of the Styrofoam collar should be recalculated. Let's do it step by step:
V_styrofoam = (π * R^2 * h) - (π * r^2 * h)
V_styrofoam = (3.14 * 6^2 * 19) - (3.14 * 5^2 * 19)
V_styrofoam = (3.14 * 36 * 19) - (3.14 * 25 * 19)
V_styrofoam = 2144.88 - 1477.5
V_styrofoam = 667.38 cubic inches
Therefore, the corrected volume of the Styrofoam collar should be 667.38 cubic inches. Thank you for pointing out the error, and I appreciate your understanding.
Given:
r = 5 in
R = 6 in
h = 19 in
π ≈ 3.14
Volume of the larger cylinder (V1):
V1 = πR^2h
V1 = 3.14 * 6^2 * 19
V1 = 3.14 * 36 * 19
V1 = 2145.84 cubic inches
Volume of the smaller cylinder (V2):
V2 = πr^2h
V2 = 3.14 * 5^2 * 19
V2 = 3.14 * 25 * 19
V2 = 4715 cubic inches
Volume of the Styrofoam collar:
V_styrofoam = V1 - V2
V_styrofoam = 2145.84 - 4715
V_styrofoam = -2569.16 cubic inches
Upon re-evaluation, it appears that there was an error in the calculation. The volume of a collar cannot be negative. Let's correct the calculation.
The correct formula to find the volume of the Styrofoam collar should involve the difference in volumes as before, but the calculation was not accurate. Let's re-calculate accurately:
V_styrofoam = V1 - V2
V_styrofoam = 2145.84 - 4715
V_styrofoam = -2569.16 cubic inches
Therefore, the volume of the Styrofoam collar should be recalculated. Let's do it step by step:
V_styrofoam = (π * R^2 * h) - (π * r^2 * h)
V_styrofoam = (3.14 * 6^2 * 19) - (3.14 * 5^2 * 19)
V_styrofoam = (3.14 * 36 * 19) - (3.14 * 25 * 19)
V_styrofoam = 2144.88 - 1477.5
V_styrofoam = 667.38 cubic inches
Therefore, the corrected volume of the Styrofoam collar should be 667.38 cubic inches. Thank you for pointing out the error, and I appreciate your understanding.