Question

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)

Answer 1

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 (2\pi )/(2+1)}{1\cdot (2\pi )/(2+1)}\implies \cfrac{~~(4\pi )/(3)~~}{(2\pi )/(3)} \\\\[-0.35em] ~\dotfill\\\\ vanilla\implies \cfrac{4\pi }{3}\qquad \approx\qquad 4.19~in^3`