Question

find the missing dimension of the cylinder. round your answer to the nearest whole number. volume = 10,000π in.³ 14 h = □ 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.

Step2: Substitute the known values into the formula

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

Step3: Simplify the equation

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

Step4: Solve for \(h\)

\(h=\frac{10000}{1024}\approx9.765625\)

Answer:

\(h\approx10\) in