Mathematics
A medicine capsule is in the shape of a cylinder with two hemispheres 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.
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Answer
From figure,
Diameter of capsule (d) = 5 mm
Radius of capsule (r) = = 2.5 mm
From figure
Radius of cylindrical portion = Radius of hemispherical portion = Radius of capsule (r) = 2.5 mm.
Height of cylindrical portion (h) = 14 - (2.5 + 2.5) = 14 - 5 = 9 mm.
Surface area of capsule = Curved surface area of cylindrical portion + 2 × Curved surface area of hemispherical portion
= 2πrh + 2 × 2πr2
= 2πrh + 4πr2
= 2πr(h + 2r)
=
=
= = 220 mm2.
Hence, surface area of capsule = 220 mm2.
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