Question

A conical paper cup has a radius of 2 inches. Approximate, to the nearest degree, the angle β so that the cone will have a volume of 20 in^3

Answer 1

\[v=\frac{1}{3} \pi r^2h \]Replace v with 20, r with 2 and then solve for h.\[\frac{4 h \pi }{3}=20 \]\[h=\frac{15}{\pi } \]The angle beta at the top of the cone is:\[\beta =2 \text{ArcTan}\left[\frac{2}{\frac{15}{\pi }}\right]*180/\pi =45.4556{}^{\circ} \]