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: Calculate the radius

The radius $r$ of the base of the cone is half of the diameter. Given diameter $d = 8$ units, so $r=\frac{d}{2}=\frac{8}{2}=4$ units.

Step2: Use the volume formula for a cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 4$ units and $h=6$ units into the formula. We get $V=\frac{1}{3}\pi\times4^{2}\times6$.
First, calculate $4^{2}=16$, then $16\times6 = 96$. So $V=\frac{1}{3}\pi\times96$.
$\frac{1}{3}\times96 = 32$, so $V = 32\pi$ cubic units.

Answer:

32$\pi$ cubic units