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

In the drawing above we can sub V=20 for the volume, and r=2 for the radius, then we can solve for the height h in the formula\[V=\frac{1}{3} \pi r^2h\]Once we have h and r, we can use inverse tangent to get beta:\[20=\frac{1}{3} \pi (2)^2h\]or\[h=\frac{15}{\pi}\approx4.775\](continued)