A medicine capsule is in the shape of a cylinder with two hemisphere stuck to each of its ends. the length of the capsule is 14mm and the width is 5mm find its surface area ?
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Answer:
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Surface area of the capsule = 2 × CSA of hemispherical part + CSA of cylindrical part
The surface area of the capsule can be found by using formulae;
CSA of the hemisphere = 2πr2, where r is the radius of the hemisphere
CSA of the cylinder = 2πrh, where r and h are the radius and height of the cylinder respectively.
Diameter of the capsule, d = 5 mm
Radius of the hemisphere, r = d/2 = 5/2 mm
Radius of the cylinder, r = 5/2 mm
Length of the cylinder = Length of the capsule - 2 × radius of the hemisphere
h = 14 mm - 2 × 5/2 mm = 9 mm
Surface area of the capsule = 2 × CSA of hemispherical part + CSA of cylindrical part
= 2 × 2πr2 + 2πrh
= 2πr (2r + h)
= [2 × 22/7 × 5/2 mm × (2 × 5/2 mm + 9 mm)]
= 110/7 mm × 14 mm
= 220 mm2
Thus, the surface area of the capsule is 220 mm2