# 6. A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig.). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

It is clear from the figure that the capsule has hemisphere and cylinder structure.

The surface area of capsule  =   2 (Area of the hemisphere)   +   Area of the cylindrical part

Area of hemisphere  $=\ 2\pi r^2$

or                              $=\ 2\pi\times \left ( \frac{5}{2} \right )^2$

or                              $=\ \frac{25}{2} \pi\ mm^2$

And the area of the cylinder   $=\ 2\pi rh$

or                               $=\ 2\pi \times \frac{5}{2}\times 9$

or                              $=\ 45 \pi\ mm^2$

Thus the area of the solid is  :

$=\ 2\left ( \frac{25}{2} \right )\pi\ +\ 45 \pi$

$=\ 25\pi\ +\ 45 \pi$

$=\ 70 \pi$

$=\ 220\ mm^2$

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