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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 mm and the diameter of the capsule is 5 mm. Find its surface area.

Let r cm be the radius and h cm be the height of the cylinder. Then.

$$r \ = \ \frac{5}{2} \ = \ 2.5$$mm

$$h \ = \ (14 \ - \ 2 \ × \ \frac{5}{2}) \ = 14 \ - \ 5 \ = \ 9$$mm

Also the radius of hemisphere $$= \ \frac{5}{2}$$ cm

Now, surface area of the capsule = Curved surface of cylinder + Surface area of two hemispheres

$$= \ 2 \pi rh \ + \ 2 \ × \ 2\pi r^2 \ = \ 2\pi r(h \ + \ 2r)$$

$$= \ 2 \ × \ \frac{22}{7} \ × \ \frac{5}{2} \ × \ (9 \ + \ 2 \ × \ \frac{5}{2}) \ = \ 220$$ mm2