A medicine capsule is in the shape of a cylinder with two hemisphere stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.
A medicine capsule is in the shape of a cylinder with two hemisphere stuck to each of its ends.
Total length of entire capsule = 14 mm
Diameter of capsule = 5 mm
Radius of capsule = r = Diameter ÷ 2 = 5/2 mm = 2.5 mm
Length of cylindrical part of capsule = l = Total length of entire capsule – 2 × Radius of capsule
= 14 – 2 × 2.5 mm = 14 - 5 mm = 9 mm
Curved surface area of cylindrical part of capsule = 2πrl
= 2 × 3.14 × 9 × 2.5 mm2
= 141.3 mm2
Curved surface area of hemispherical ends = 2 × 2πr2
= 2 × 2 × 3.14 × 2.5 × 2.5 cm2
= 78.5 mm2
Surface area of capsule = Curved surface area of cylindrical part of capsule + Curved surface area of hemispherical ends
Surface area of capsule = 141.3 mm2 + 78.5 mm2 = 219.8 mm2