Question

what is the volume of a cylinder with base radius 3 and height 6? either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal. (there is a diagram of a cylinder with radius 3 and height 6)

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 \( r = 3 \) and \( h=6 \). Substituting these values into the formula, we get \( V=\pi\times(3)^{2}\times6 \).

Step3: Simplify the expression

First, calculate \( 3^{2}=9 \). Then, multiply \( 9\times6 = 54 \). So, \( V = 54\pi \). If we use \( \pi=3.14 \), then \( V=3.14\times54 \). Calculating \( 3.14\times54 \): \( 3\times54 = 162 \), \( 0.14\times54=7.56 \), and \( 162 + 7.56=169.56 \).

Answer:

If in terms of \( \pi \), the answer is \( 54\pi \); if using \( 3.14 \) for \( \pi \), the answer is \( 169.56 \)