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Question
A capsule is in the shape of a cylinder with two hemispheres stuck to its ends. If the length of the entire capsule is 12 mm and the diameter of the capsule is 3 mm, how much medicine it can hold?
Solution
Radius of a hemisphere = Radius of a Cylinder
r = `3/2` mm = 1.5 mm
Height of the cylinderical portion
= 12 mm – (1.5 mm + 1.5 mm)
= (12 – 3) mm
= 9 mm
Volume of the capsule
= `pi"r"^2"h" + 2 xx 2/3 pi"r"^3`
= `pi"r"^2 ("h" + 4/3"r")`
= `22/7 xx 1.5 xx 1.5 (9 + 4/3 xx 1.5)`
= `22/7 xx 1.5 xx 1.5(9 + 2)`
= `22/7 xx 1.5 xx 1.5 xx 11 "mm"^3`
= 77.8 cu.mm
Volume of the capsule = 77.8 cu.mm
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