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Mathematics Question on Surface Area of a Combination of Solids

A medicine capsule is in the shape of cylinder with two hemispheres stuck to each of its ends (see the given figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area. [Use π=227\pi=\frac{22 }{7}
A medicine capsule is in the shape of cylinder with two hemispheres stuck to each of its ends

Answer

A medicine capsule is in the shape of cylinder with two hemispheres stuck to each of its ends

It can be observed that Radius (r) of cylindrical part = Radius (r) of hemispherical part
=Distance  of  the  capsule2=52=\frac{\text{Distance}\ \text{ of}\ \text{ the }\ \text{capsule}}{2}=\frac{5}{2}

Length of cylindrical part (h) = Length of the entire capsule −2×r=14−5=9− 2 × r = 14 − 5 = 9 cm

Surface area of capsule =2×= 2×CSA of hemispherical part + CSA of cylindrical part
=2×2πr2+2πrh= 2×2\pi r^2 +2\pi rh

=2×(227)×2.5×2.5+2×(227)×2.5×9=2×(\frac{22}{7})×2.5×2.5+2×(\frac{22}{7})×2.5×9

=(2×2757)×9907= (2×\frac{275}{7}) × \frac{990}{7}

=(5507)+(9907)=15407=220= (\frac{550}{7}) + (\frac{990}{7}) = \frac{1540}{7} = 220 mm2