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geometry

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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

Jun 28, 2020

#1
+8352
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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.

Jun 28, 2020