Problem

For the steel pipe shown, the wall thickness is $1 / 4$ inch and the outer diameter is 2 inches. If the pipe is 1 foot long, what volume of steel is it made of?

Answer

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Answer

Final Answer: The volume of the steel the pipe is made of is approximately \(\boxed{16.49}\) cubic inches.

Steps

Step 1 :Given that the outer diameter of the steel pipe is 2 inches, the wall thickness is $\frac{1}{4}$ inch, and the length of the pipe is 1 foot (or 12 inches).

Step 2 :The outer radius of the pipe is half of the outer diameter, which is 1 inch. The inner radius of the pipe is the outer radius minus the wall thickness, which is $1 - \frac{1}{4} = \frac{3}{4}$ inch.

Step 3 :The volume of a cylinder is given by the formula $\pi r^2 h$, where $r$ is the radius and $h$ is the height (or length in this case).

Step 4 :Calculate the volume of the outer cylinder using the formula $\pi r^2 h$, where $r$ is the outer radius (1 inch) and $h$ is the length of the pipe (12 inches). This gives a volume of approximately 37.699 cubic inches.

Step 5 :Calculate the volume of the inner cylinder using the formula $\pi r^2 h$, where $r$ is the inner radius ($\frac{3}{4}$ inch) and $h$ is the length of the pipe (12 inches). This gives a volume of approximately 21.206 cubic inches.

Step 6 :The volume of the steel the pipe is made of is the difference between the volume of the outer cylinder and the volume of the inner cylinder. This is approximately $37.699 - 21.206 = 16.493$ cubic inches.

Step 7 :Final Answer: The volume of the steel the pipe is made of is approximately \(\boxed{16.49}\) cubic inches.

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