Question

a cylinder has a radius of 12 m and a height of 9 m. what is the exact volume of the cylinder? \\(\bigcirc\\) \\(108\pi\\ m^3\\) \\(\bigcirc\\) \\(216\pi\\ m^3\\) \\(\bigcirc\\) \\(972\pi\\ m^3\\) \\(\bigcirc\\) \\(1296\pi\\ m^3\\)

Explanation:

Step1: Recall the formula for the volume of a cylinder

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

Step2: Substitute the given values into the formula

We are given that \( r = 12 \, \text{m} \) and \( h = 9 \, \text{m} \). First, calculate \( r^2 \): \( r^2=(12)^2 = 144 \). Then substitute \( r^2 = 144 \) and \( h = 9 \) into the volume formula: \( V=\pi\times144\times9 \).

Step3: Calculate the product

Calculate \( 144\times9 \). \( 144\times9 = 1296 \). So the volume \( V = 1296\pi \, \text{m}^3 \).

Answer:

\( 1296\pi \, \text{m}^3 \) (corresponding to the option: 1296π m³)