Answer to Question #124936 in Geometry for Jonathan

Question

Given a soda can with a volume of 15 and a diameter of 2, what is the volume of a cone that fits perfectly inside the soda can? (Hint: only enter whole numbers in the answer blank). Numerical Answers Expected

Answer 1

$$\textnormal{Let's imagine how a cone can be located} \\ \textnormal{to occupy the maximum volume. } \\ \textnormal{ Their bases and heights must be equal.} \\ \textnormal{Let's write the known volume formulas} \\ \textnormal{and calculate the answer} \\ V_{cylinder} = S * h \implies h = \frac {V_{cylinder}} {S} \\ V_{cone} = \frac{1}{3}*S*h=\frac{1}{3}*S*\frac {V_{cylinder}} {S} \\ V_{cone} = \frac{1}{3}*\cancel{S}*\frac {V_{cylinder}} {\cancel{S}} = \frac{1}{3}*V_{cylinder} \\ V_{cone} = \frac{1}{3}*15=5$$