Question

the volume of this cylinder is 3,416.32 cubic centimeters. what is the height?
round your answer to the nearest hundredth.
8 cm
h
centimeters
submit

Explanation:

Step1: Recall the volume formula of a cylinder

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

Step2: Substitute the known values into the formula

Given \(V = 3416.32\) cubic centimeters and \(r=8\) centimeters. Substitute into \(V=\pi r^{2}h\), we get \(3416.32=\pi\times8^{2}\times h\).
First, calculate \(8^{2}=64\). Then the equation becomes \(3416.32 = 3.14\times64\times h\) (taking \(\pi\approx3.14\)).
Calculate \(3.14\times64 = 200.96\). So the equation is \(3416.32=200.96h\).

Step3: Solve for \(h\)

Divide both sides of the equation \(3416.32 = 200.96h\) by \(200.96\).
\(h=\frac{3416.32}{200.96}\).
\(h = 17.00\)

Answer:

\(17.00\)