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A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see figure). The length of the entire capsule is $14\,\mathrm{mm}$ and the diameter of the capsule is $5\,\mathrm{mm}$. Find its surface area. 
A$165\,\mathrm{mm}^2$
B$220\,\mathrm{mm}^2$
C$110\,\mathrm{mm}^2$
D$192.5\,\mathrm{mm}^2$
Answer & Solution
Correct answer: A. $165\,\mathrm{mm}^2$
Radius $r=2.5\,\mathrm{mm}$. The cylindrical part has length $14-2r=14-5=9\,\mathrm{mm}$. Surface area $=$ CSA of cylinder $+$ CSA of two hemispheres $=2\pi rh+4\pi r^2=2\pi(2.5)(9)+4\pi(2.5)^2=45\pi+25\pi=70\pi=220\,\mathrm{mm}^2$ using $\pi=\frac{22}{7}$. So the correct value is $220\,\mathrm{mm}^2$.
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