Question

the diameter of the base of the cone measures 8 units. the height measures 6 units. what is the volume of the cone? 24π cubic units 32π cubic units 48π cubic units 64π cubic units

Explanation:

Step1: Find the radius of the base

The diameter of the base is 8 units, so the radius \( r \) is half of the diameter.
\( r=\frac{8}{2}=4 \) units.

Step2: Recall the volume formula for a cone

The volume \( V \) of a cone is given by the formula \( V = \frac{1}{3}\pi r^{2}h \), where \( r \) is the radius of the base and \( h \) is the height of the cone.

Step3: Substitute the values of \( r \) and \( h \) into the formula

We know that \( r = 4 \) units and \( h=6 \) units. Substituting these values into the formula:
\( V=\frac{1}{3}\pi\times(4)^{2}\times6 \)

Step4: Simplify the expression

First, calculate \( (4)^{2}=16 \). Then, multiply \( 16 \) and \( 6 \): \( 16\times6 = 96 \). Then, multiply by \( \frac{1}{3} \): \( \frac{1}{3}\times96=32 \). So, \( V = 32\pi \) cubic units.

Answer:

32π cubic units (corresponding to the option: 32π cubic units)