a hollow cylindrical pipe is 21m long .its outer and inner diameters are 10 cm and 6cm respectively .find the volume of copper used in making the pipe?/
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To find the volume of copper used in making the pipe, we need to calculate the difference between the volume of the outer cylinder and the volume of the inner cylinder.
1. Calculate the volumes of the outer and inner cylinders:
- Volume of the outer cylinder = π * (radius^2) * height
- Volume of the inner cylinder = π * (radius^2) * height
2. Convert the given dimensions into meters:
- Outer radius = 10 cm = 0.1 m
- Inner radius = 6 cm = 0.06 m
- Height = 21 m
3. Calculate the volume of the outer and inner cylinders:
- Volume of the outer cylinder = π * (0.1^2) * 21
- Volume of the inner cylinder = π * (0.06^2) * 21
4. Subtract the volume of the inner cylinder from the volume of the outer cylinder to find the volume of copper used:
- Volume of copper used = Volume of the outer cylinder - Volume of the inner cylinder
Now, let's calculate the volume of copper used in making the pipe step by step:
Step 1: Calculate the volume of the outer cylinder:
Volume of the outer cylinder = π * (0.1^2) * 21
= 0.1 * 0.1 * 21 * π
≈ 0.066 m^3 (rounded to 3 decimal places)
Step 2: Calculate the volume of the inner cylinder:
Volume of the inner cylinder = π * (0.06^2) * 21
= 0.06 * 0.06 * 21 * π
≈ 0.023 m^3 (rounded to 3 decimal places)
Step 3: Calculate the volume of copper used:
Volume of copper used = Volume of the outer cylinder - Volume of the inner cylinder
= 0.066 - 0.023
≈ 0.043 m^3 (rounded to 3 decimal places)
Therefore, the volume of copper used in making the pipe is approximately 0.043 cubic meters.