A chocolate shop sells its products in 3 different shapes: a cylindrical bar, a spherical ball, and a cone. These 3 shapes are of the same height and radius, as shown in the picture. Which of these choices would give you the most chocolate?
I. A full cylindrical bar
II. A ball plus a cone
+9519 Using the formula to find the volumes, we have
\(V_{\text{cylinder}} = \pi r^2 \cdot 2r = 2\pi r^3\\ V_{\text{sphere}} = \dfrac43 \pi r^3\\ V_{\text{cone}} = \dfrac13 V_{\text{cylinder}} = \dfrac23 \pi r^3\)
We have \(V_{\text{cylinder}} = 2\pi r^3\) and \(V_{\text{cylinder}} + V_{\text{cone}} = \dfrac43 \pi r^3 + \dfrac23 \pi r^3 = 2\pi r^3\), so the two choices gives the same amount of chocolate.
