Question

what is the volume, in cubic meters, of a cylinder with a height of 16 meters and a base radius of 8 meters, to the nearest tenths place?

Explanation:

Step1: Recall the formula for the volume of a cylinder

The formula for the volume \(V\) of a cylinder is \(V=\pi r^{2}h\), where \(r\) is the radius of the base and \(h\) is the height.

Step2: Substitute the given values into the formula

Given \(r = 8\) meters and \(h=16\) meters. Substitute these values into the formula: \(V=\pi\times(8)^{2}\times16\).
First, calculate \((8)^{2}=64\). Then \(V=\pi\times64\times16\).
\(64\times16 = 1024\), so \(V = 1024\pi\).

Step3: Calculate the numerical value

Using \(\pi\approx3.14159\), we have \(V\approx1024\times3.14159\).
\(1024\times3.14159=(1000 + 24)\times3.14159=1000\times3.14159+24\times3.14159\).
\(1000\times3.14159 = 3141.59\), \(24\times3.14159=75.39816\).
\(V\approx3141.59+75.39816=3216.98816\).

Step4: Round to the nearest tenths place

To round \(3216.98816\) to the nearest tenths place, look at the digit in the hundredths place. The digit in the hundredths place is \(8\). Since \(8>5\), we round up the digit in the tenths place.
\(3216.98816\approx3217.0\)

Answer:

\(3217.0\) cubic meters