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 base radius

The diameter is 8, so radius $r = \frac{8}{2} = 4$ units.

Step2: Recall cone volume formula

Volume formula: $V = \frac{1}{3}\pi r^2 h$

Step3: Substitute values and calculate

Substitute $r=4$, $h=6$:

$$\begin{align*} V&=\frac{1}{3}\pi (4)^2 (6)\\ &=\frac{1}{3}\pi \times 16 \times 6\\ &=\pi \times 16 \times 2\\ &=32\pi \end{align*}$$

Answer:

32π cubic units