Question

1. if a cylinder has a radius of 4 units and a height of 8 units, what is its volume in terms of π?

a. v = 128π cubic units
b. v = 64π cubic units
c. v = 96π cubic units
d. v = 32π cubic units

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

Given \( r = 4 \) units and \( h=8 \) units. Substitute into \( V=\pi r^{2}h \), we get \( V=\pi\times(4)^{2}\times8 \).

Step3: Calculate \( (4)^{2} \)

\( (4)^{2}=4\times4 = 16 \). So the formula becomes \( V=\pi\times16\times8 \).

Step4: Calculate \( 16\times8 \)

\( 16\times8=128 \). So \( V = 128\pi \) cubic units.

Answer:

A. \( V = 128\pi \) cubic units