Question

1. the exact volume of a cylinder is 80π in³. if the radius is 4 cm, what will be the height of the cylinder?

Explanation:

Step1: Recall cylinder volume formula

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

Step2: Substitute known values

We know \( V = 80\pi\) \( in^{3} \) and \( r = 4 \) cm. Substitute these into the formula: \( 80\pi=\pi\times(4)^{2}\times h \).

Step3: Simplify and solve for h

First, simplify \( (4)^{2}=16 \), so the equation becomes \( 80\pi=\pi\times16\times h \). Divide both sides by \( \pi \): \( 80 = 16h \). Then divide both sides by 16: \( h=\frac{80}{16}=5 \).

Answer:

The height of the cylinder is 5 cm.