Question

question 3
a cylinder has a volume of 100π cm³ and a radius of 5 cm.
the height is 4 cm.
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Explanation:

Step1: Recall the volume formula for a cylinder

The volume formula for 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 given values into the formula

We know that \( V = 100\pi\) \(cm^{3}\) and \( r = 5\) \(cm\). Substituting these into \( V=\pi r^{2}h\) gives \(100\pi=\pi\times(5)^{2}\times h\).

Step3: Simplify the equation

First, simplify \(\pi\times(5)^{2}\) to \(25\pi\). So the equation becomes \(100\pi = 25\pi h\).

Step4: Solve for \( h \)

Divide both sides of the equation \(100\pi = 25\pi h\) by \(25\pi\). \(\frac{100\pi}{25\pi}=h\). Since \(\frac{100}{25}=4\) and \(\frac{\pi}{\pi} = 1\) (for \(\pi
eq0\)), we get \(h = 4\) \(cm\).

Answer:

\(4\)