Question

what is the volume, in cubic feet, of a cylinder with a height of 8 feet and a base radius of 5 feet, 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 of the cylinder.

Step2: Substitute the given values into the formula

We are given that \( r = 5 \) feet and \( h=8 \) feet. Substituting these values into the formula, we get \( V=\pi\times(5)^{2}\times8 \).
First, calculate \( (5)^{2}=25 \). Then, multiply by 8: \( 25\times8 = 200 \). So now the volume is \( V = 200\pi \).

Step3: Calculate the numerical value and round to the nearest tenth

Using the approximation \( \pi\approx3.14159 \), we have \( V=200\times3.14159 = 628.318 \). Rounding \( 628.318 \) to the nearest tenth, we look at the hundredth place, which is 1. Since \( 1<5 \), we round down, so the volume is approximately \( 628.3 \).

Answer:

\( 628.3 \) cubic feet