Question

the radius of the base of a right cylinder is 12 cm, and the height of the cylinder is 18 cm. in terms of π, what is the volume of the cylinder? a 216π cm³ b 1,438π cm³ c 2,592π cm³ d 3,888π cm³

Explanation:

Step1: Recall the formula for the volume of a cylinder

The volume \( V \) of a right 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 \( r = 12 \, \text{cm} \) and \( h = 18 \, \text{cm} \). Substituting these values into the formula, we get:
\[
V=\pi\times(12)^2\times18
\]

Step3: Calculate \( (12)^2 \)

First, calculate \( 12^2 = 144 \). So the formula becomes:
\[
V=\pi\times144\times18
\]

Step4: Multiply 144 and 18

Now, multiply \( 144 \) and \( 18 \). \( 144\times18 = 2592 \). So the volume is:
\[
V = 2592\pi \, \text{cm}^3
\]

Answer:

C. \( 2592\pi \, \text{cm}^3 \)