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A right circular cylinder circumscribes the toy made of a cone on a hemisphere, shown in the figure. The toy has radius $2\,\mathrm{cm}$ and cone height $2\,\mathrm{cm}$. What is the difference between the volume of the circumscribing cylinder and the volume of the toy? Use $\pi=3.14$. 
A$12.56\,\mathrm{cm}^3$
B$18.84\,\mathrm{cm}^3$
C$25.12\,\mathrm{cm}^3$
D$50.24\,\mathrm{cm}^3$
Answer & Solution
Correct answer: C. $25.12\,\mathrm{cm}^3$
The circumscribing cylinder has the same radius $2\,\mathrm{cm}$ and total height equal to cone height $+$ hemisphere radius $=2+2=4\,\mathrm{cm}$. So its volume is $\pi r^2h=3.14\times2^2\times4=50.24\,\mathrm{cm}^3$. The toy volume is $25.12\,\mathrm{cm}^3$, so the difference is $50.24-25.12=25.12\,\mathrm{cm}^3$.
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