Question

b. the height of a cylinder is 7.2 m. the radius of the base is 4m. find the exact volume of the cylinder.

Explanation:

Step1: Recall the formula for the volume of a cylinder

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

Step2: Substitute the given values into the formula

We are given that \( r = 4\space m \) and \( h=7.2\space m \). Substituting these values into the formula, we get:
\( V=\pi\times(4)^{2}\times7.2 \)
First, calculate \( 4^{2}=16 \). Then, multiply \( 16 \) by \( 7.2 \): \( 16\times7.2 = 115.2 \)
So, \( V = 115.2\pi\space m^{3} \) (or if we want to write \( 7.2=\frac{36}{5} \) and \( 4^{2} = 16\), then \( V=\pi\times16\times\frac{36}{5}=\frac{576}{5}\pi= 115.2\pi\))

Answer:

The exact volume of the cylinder is \( 115.2\pi\space m^{3} \) (or \( \frac{576}{5}\pi\space m^{3} \))