An ice cream cone is filled with 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? (round to nearest tenth)
1 answer:
since the diameter of the cone is 2 inches, then its radius is half that, namely 1 inch, thus
![\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=1\\ h=6 \end{cases}\implies V=\cfrac{\pi (1)^2(6)}{3}\implies V=2\pi \\\\[-0.35em] ~\dotfill\\\\ \cfrac{vanilla}{chocolate}\qquad 2:1\qquad \cfrac{2}{1}\qquad \qquad \cfrac{2\cdot \frac{2\pi }{2+1}}{1\cdot \frac{2\pi }{2+1}}\implies \cfrac{~~\frac{4\pi }{3}~~}{\frac{2\pi }{3}} \\\\[-0.35em] ~\dotfill\\\\ vanilla\implies \cfrac{4\pi }{3}\qquad \approx\qquad 4.19~in^3](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bvolume%20of%20a%20cone%7D%5C%5C%5C%5C%20V%3D%5Ccfrac%7B%5Cpi%20r%5E2%20h%7D%7B3%7D~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%20h%3Dheight%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D1%5C%5C%20h%3D6%20%5Cend%7Bcases%7D%5Cimplies%20V%3D%5Ccfrac%7B%5Cpi%20%281%29%5E2%286%29%7D%7B3%7D%5Cimplies%20V%3D2%5Cpi%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7Bvanilla%7D%7Bchocolate%7D%5Cqquad%202%3A1%5Cqquad%20%5Ccfrac%7B2%7D%7B1%7D%5Cqquad%20%5Cqquad%20%5Ccfrac%7B2%5Ccdot%20%5Cfrac%7B2%5Cpi%20%7D%7B2%2B1%7D%7D%7B1%5Ccdot%20%5Cfrac%7B2%5Cpi%20%7D%7B2%2B1%7D%7D%5Cimplies%20%5Ccfrac%7B~~%5Cfrac%7B4%5Cpi%20%7D%7B3%7D~~%7D%7B%5Cfrac%7B2%5Cpi%20%7D%7B3%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20vanilla%5Cimplies%20%5Ccfrac%7B4%5Cpi%20%7D%7B3%7D%5Cqquad%20%5Capprox%5Cqquad%204.19~in%5E3)
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