Question

a cylinder has a height of 12 yards and a diameter of 18 yards. what is its volume? round your answer to the nearest hundredth. cubic yards

Explanation:

Step1: Find the radius

The diameter \(d = 18\) yards. The radius \(r=\frac{d}{2}\), so \(r=\frac{18}{2}=9\) yards.

Step2: Use the volume formula for a cylinder

The volume formula for a cylinder is \(V=\pi r^{2}h\). Substitute \(r = 9\) yards and \(h=12\) yards.
\(V=\pi\times(9)^{2}\times12\)
First, calculate \((9)^{2}=81\). Then \(V=\pi\times81\times12\).
\(81\times12 = 972\), so \(V = 972\pi\).
Using \(\pi\approx3.14159\), \(V\approx972\times3.14159\).
\(972\times3.14159=972\times(3 + 0.14159)=972\times3+972\times0.14159\)
\(972\times3 = 2916\), \(972\times0.14159=(1000 - 28)\times0.14159=1000\times0.14159-28\times0.14159\)
\(1000\times0.14159 = 141.59\), \(28\times0.14159=3.96452\)
\(141.59-3.96452 = 137.62548\)
\(2916+137.62548=3053.62548\approx3053.63\)

Answer:

\(3053.63\)