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.

                                          

Answers (1)

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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