Question

problem 7 here is a cylinder with a radius of 4 feet and a height of 9 feet. what is the volume of the cylinder in cubic feet? round your answer to the nearest hundredth.

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 and \( h \) is the height.

Step2: Identify the values of \( r \) and \( h \)

Given that the radius \( r = 4 \) feet and the height \( h=9 \) feet.

Step3: Substitute the values into the formula

Substitute \( r = 4 \) and \( h = 9 \) into the formula \( V=\pi r^{2}h \), we get \( V=\pi\times(4)^{2}\times9 \).
First, calculate \( 4^{2}=16 \), then \( 16\times9 = 144 \), so \( V = 144\pi \).

Step4: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have \( V\approx144\times3.14159 \).
\( 144\times3.14159 = 452.38944 \).

Step5: Round to the nearest hundredth

Rounding \( 452.38944 \) to the nearest hundredth, we look at the thousandth digit which is 9. Since \( 9\gt5 \), we round up the hundredth digit. So \( 452.38944\approx452.39 \).

Answer:

\( 452.39 \) cubic feet