Question

the diameter of a cylindrical construction pipe is 3 ft. if the pipe is 12 ft long, what is its volume? use the value 3.14 for π, and round your answer to the nearest whole number. be sure to include the correct unit in your answer.

Explanation:

Step1: Find the radius of the cylinder

The diameter \( d = 3\) ft, so the radius \( r=\frac{d}{2}=\frac{3}{2} = 1.5\) ft.

Step2: Recall the formula for the volume of a cylinder

The volume \( V\) of a cylinder is given by the formula \( V=\pi r^{2}h\), where \( r\) is the radius and \( h\) is the height (or length in this case). Here, \( h = 12\) ft and \(\pi=3.14\).

Step3: Substitute the values into the formula

First, calculate \( r^{2}=(1.5)^{2}=2.25\). Then, \( V = 3.14\times2.25\times12\).
Calculate \( 3.14\times2.25 = 7.065\). Then, \( 7.065\times12=84.78\).

Step4: Round to the nearest whole number

Rounding \( 84.78\) to the nearest whole number gives \( 85\). The unit of volume for a cylinder (with linear units in feet) is cubic feet (\(ft^{3}\)).

Answer:

\(85\) cubic feet or \(85\ ft^{3}\)