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The decorative block shown in the figure is made of a cube of edge $5\,\mathrm{cm}$ and a hemisphere of diameter $4.2\,\mathrm{cm}$ fixed on top. Taking $\pi=\frac{22}{7}$, what is the total surface area of the block? 
A$150\,\mathrm{cm}^2$
B$163.86\,\mathrm{cm}^2$
C$177.72\,\mathrm{cm}^2$
D$136.14\,\mathrm{cm}^2$
Answer & Solution
Correct answer: B. $163.86\,\mathrm{cm}^2$
Surface area of cube $=6\times5^2=150\,\mathrm{cm}^2$. The circular region where the hemisphere is attached is not exposed, so subtract the base area of the hemisphere and add its curved surface area: $150-\pi r^2+2\pi r^2=150+\pi r^2$. Here $r=2.1\,\mathrm{cm}$, so area $=150+\frac{22}{7}\times2.1\times2.1=163.86\,\mathrm{cm}^2$.
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