Final answer:
The volume of the Styrofoam insulation is calculated by finding the volume of the material around the pipe. This involves calculating the volume of the outer and inner cylinders using their respective radii and the given height and subtracting the inner volume from the outer volume.
Step-by-step explanation:
The volume of the Styrofoam insulation for a pipe can be calculated using the formula for the volume of a cylinder V = πr²h. However, since the Styrofoam forms a collar around the pipe, we need to find the volume of the outer cylinder (Styrofoam plus pipe) and subtract the volume of the inner cylinder (the pipe itself) to get the volume of just the Styrofoam insulation.
The volume V of the outer cylinder is calculated using the outer radius R, which is 6 inches:
Vouter = π * R² * h = π * 6² * 20
The volume V of the inner cylinder is calculated using the inner radius r, which is 5 inches:
Vinner = π * r² * h = π * 5² * 20
Now, subtract the inner volume from the outer volume to get the volume of the insulation:
Volume of insulation = Vouter - Vinner
Calculating the volumes:
- Vouter = π * 36 * 20 = 720π cubic inches
- Vinner = π * 25 * 20 = 500π cubic inches
- Volume of insulation = 720π - 500π = 220π cubic inches
Using π as approximately 3.14159, we calculate:
Volume of insulation ≈ 220 * 3.14159 ≈ 691.1498 cubic inches
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