Answer: 137.25π ≈ 431.18 cm³
Step-by-step explanation:
Entire Cone - Tip of Cone = Frustrum
[tex]V_{cone}=\dfrac{1}{3}\pi r^2h\\\\\\V_{Entire}=\dfrac{1}{3}\pi (6)^2(12)\quad =\quad 144\pi\\\\V_{Tip}=\dfrac{1}{3}\pi \bigg(\dfrac{6}{4}\bigg)^2\bigg(\dfrac{12}{4}\bigg)\quad =\quad \dfrac{27}{4}\pi\\\\\\\\V_{Frustrum}=V_{Entire}-V_{Tip}\\\\.\qquad \qquad =144\pi-\dfrac{27}{4}\pi\\\\.\qquad \qquad =\dfrac{549}{4}\pi\\\\.\qquad \qquad =137.25\pi\\\\.\qquad \qquad=\large\boxed{431.18}[/tex]
