Q. 19

# 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

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