Question

a cylinder has a radius of 11 centimeters. its volume is 6,914.908 cubic centimeters. what is the height of the cylinder? use π ≈ 3.14 and round your answer to the nearest hundredth. h ≈ □ centimeters submit

Explanation:

Step1: Recall the volume formula for a cylinder

The volume \( V \) of a cylinder is given by the formula \( V=\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height. We need to solve for \( h \), so we can rearrange the formula to \( h = \frac{V}{\pi r^{2}} \).

Step2: Substitute the given values into the formula

We know that \( V = 6914.908 \) cubic centimeters, \( r = 11 \) centimeters, and \( \pi\approx3.14 \). First, calculate \( r^{2} \): \( r^{2}=11^{2} = 121 \). Then calculate \( \pi r^{2} \): \( \pi r^{2}\approx3.14\times121=379.94 \).

Step3: Solve for \( h \)

Now, substitute \( V \) and \( \pi r^{2} \) into the formula for \( h \): \( h=\frac{6914.908}{379.94} \). Performing the division: \( \frac{6914.908}{379.94}=18.2 \).

Answer:

\( 18.20 \) (rounded to the nearest hundredth)