The problem asks to find the exact volume of a cylindrical pipe with radius $r = 4.5$ ft and length $h = 7$ ft. The answer needs to be expressed in terms of $\pi$.

GeometryVolumeCylinderFormulaUnits
2025/4/14

1. Problem Description

The problem asks to find the exact volume of a cylindrical pipe with radius r=4.5r = 4.5 ft and length h=7h = 7 ft. The answer needs to be expressed in terms of π\pi.

2. Solution Steps

The formula for the volume of a cylinder is:
V=πr2hV = \pi r^2 h
Substitute the given values into the formula:
V=π(4.5)2(7)V = \pi (4.5)^2 (7)
Calculate (4.5)2(4.5)^2:
(4.5)2=4.5×4.5=20.25(4.5)^2 = 4.5 \times 4.5 = 20.25
Substitute this value back into the volume formula:
V=π(20.25)(7)V = \pi (20.25)(7)
Multiply 20.2520.25 by 77:
20.25×7=141.7520.25 \times 7 = 141.75
Therefore, the volume is:
V=141.75πV = 141.75\pi

3. Final Answer

141.75π141.75\pi

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