Question

find the missing dimension of the cylinder. round your answer to the nearest whole number.
volume = 10,000π in.³
32 in.
h
4
10
in.

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. Given \(V = 10000\pi\) in\(^{3}\) and \(r=32\) in.

Step2: Substitute the known values into the formula

Substitute \(V = 10000\pi\) and \(r = 32\) into \(V=\pi r^{2}h\). We get \(10000\pi=\pi\times32^{2}\times h\).

Step3: Simplify the equation

Divide both sides of the equation \(10000\pi=\pi\times32^{2}\times h\) by \(\pi\). The equation becomes \(10000 = 32^{2}\times h\). Since \(32^{2}=1024\), the equation is \(10000=1024h\).

Step4: Solve for \(h\)

Solve for \(h\) by \(h=\frac{10000}{1024}\). \(h=\frac{10000\div16}{1024\div16}=\frac{625}{64}\approx9.77\).

Answer:

\(10\) in.