An ice cream cone is filled with a vanilla and chocolate ice cream at a ratio of 2:1 if the diameter of the cone is 2 inches and the height is 6 inches approximately what is the volume of vanilla ice cream in the cone

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=radius\\ h=height\\ ----------\\ diameter=2\\ r=\frac{diameter}{2}\\ \quad = 1\\ h=6 \end{cases}\implies V=\cfrac{\pi\cdot 1^2\cdot 6}{3} \\\\\\ V=2\pi \\\\ -------------------------------[/tex]

[tex]\bf \cfrac{\stackrel{vanilla}{volume}}{\stackrel{chocolate}{volume}}\qquad 2:1\qquad \cfrac{2}{1}\implies \cfrac{2\cdot \frac{V}{2+1}}{1\cdot \frac{V}{2+1}}\implies \cfrac{2\cdot \frac{2\pi }{2+1}}{1\cdot \frac{2\pi }{2+1}} \\\\\\ \cfrac{2\cdot \frac{2\pi }{3}}{1\cdot \frac{2\pi }{3}}\implies \cfrac{\quad \frac{4\pi }{3}\quad }{\frac{2\pi }{3}}[/tex]