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A solid toy consists of a hemisphere surmounted by a right circular cone. The cone height is $2\,\mathrm{cm}$ and the common base diameter is $4\,\mathrm{cm}$. What is 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 common radius is $r=2\,\mathrm{cm}$. Volume of toy $=$ volume of hemisphere $+$ volume of cone $=\frac{2}{3}\pi r^3+\frac{1}{3}\pi r^2h$. Substituting gives $\frac{2}{3}\times3.14\times8+\frac{1}{3}\times3.14\times4\times2=25.12\,\mathrm{cm}^3$.
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