Question

find the volume of the cylinder given the height and radius shown. note that the figure is not to scale. round your answer to the nearest hundredth if necessary. 14 13

Explanation:

Step1: Recall the formula for the volume of a cylinder

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

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

From the diagram, the radius \( r = 13 \) and the height \( h=14 \).

Step3: Substitute the values into the formula

Substitute \( r = 13 \) and \( h = 14 \) into the formula \( V=\pi r^{2}h \).
First, calculate \( r^{2} \): \( r^{2}=13^{2}=169 \).
Then, multiply by \( h \): \( 169\times14 = 2366 \).
Finally, multiply by \( \pi \): \( V=\pi\times2366\approx3.14159\times2366 \).

Step4: Calculate the numerical value

\( 3.14159\times2366\approx7430.90 \) (rounded to the nearest hundredth).

Answer:

The volume of the cylinder is approximately \( 7430.90 \) (if we use \( \pi\approx3.14159 \)) or more precisely, using \( \pi \) as a symbol, the volume is \( 2366\pi\approx7430.90 \).