Question

a cylinder has a radius of 6 inches and is 15 inches tall. what is the volume of the cylinder? express the answer in terms of π.
recall the formula ( v=pi r^{2}h ).

Explanation:

Step1: Substitute the values into the formula

Given the formula for the volume of a cylinder \( V=\pi r^{2}h \), where \( r = 6\) inches and \( h=15\) inches. Substitute these values: \( V=\pi\times(6)^{2}\times15 \).

Step2: Calculate \( r^{2} \)

First, calculate \( (6)^{2}=6\times6 = 36 \). So the formula becomes \( V=\pi\times36\times15 \).

Step3: Multiply the constants

Then, multiply \( 36\times15\). \(36\times15=(30 + 6)\times15=30\times15+6\times15=450+90 = 540\).

Answer:

\(540\pi\) in.\(^{3}\)