Question

a cylinder has a height of 12 feet and a radius of 11 feet. what is its volume? round your answer to the nearest hundredth. cubic feet

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: Substitute the given values into the formula

Given \( r = 11\) feet and \( h=12\) feet. Substitute into \( V=\pi r^{2}h\):
\( V=\pi\times(11)^{2}\times12\).
First, calculate \( (11)^{2}=121\). Then \( V=\pi\times121\times 12\).
\(121\times12 = 1452\), so \( V = 1452\pi\).

Step3: Calculate the numerical value

Using \( \pi\approx3.14159265\), then \( V=1452\times3.14159265\).
\(1452\times3.14159265=1452\times(3 + 0.14159265)=1452\times3+1452\times0.14159265\).
\(1452\times3 = 4356\), \(1452\times0.14159265\approx205.6936\).
\(V\approx4356+205.6936 = 4561.6936\approx4561.69\) (rounded to the nearest hundredth).

Answer:

\(4561.69\)