Question

what is the volume of a cylinder, in cubic feet, with a height of 16 feet and a base diameter of 16 feet? round to the nearest tenths place.
answer attempt 1 out of 2
v = ft³ submit answer

Explanation:

Step1: Find the radius

The diameter \(d = 16\) feet. The radius \(r=\frac{d}{2}\), so \(r=\frac{16}{2}=8\) feet.

Step2: Use the volume formula for a cylinder

The volume formula for a cylinder is \(V=\pi r^{2}h\). Here, \(r = 8\) feet and \(h=16\) feet.
Substitute the values into the formula: \(V=\pi\times(8)^{2}\times16\).
First, calculate \((8)^{2}=64\). Then \(V=\pi\times64\times16\).
\(64\times16 = 1024\), so \(V = 1024\pi\).
Using \(\pi\approx3.14159\), we have \(V\approx1024\times3.14159\).
\(1024\times3.14159=1024\times(3 + 0.14159)=1024\times3+1024\times0.14159\)
\(1024\times3 = 3072\), \(1024\times0.14159=(1000 + 24)\times0.14159=1000\times0.14159+24\times0.14159\)
\(1000\times0.14159 = 141.59\), \(24\times0.14159=3.39816\)
\(141.59+3.39816 = 144.98816\)
\(3072+144.98816=3216.98816\approx3217.0\)

Answer:

\(3217.0\)