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Question
A medicine capsule is in the shape of a cylinder of diameter 0.5 cm with a hemisphere tucked at each end. The length of the entire capsule is 2 cm. The capacity of the capsule is
Solution
0.36 cm3
Radius of the capsule `= 0.5/2 "cm"`
= 0.25 cm
Let the length of the cylindrical part of the capsule be x cm.
Then,
0.25 + x + 0.25 = 2
⇒ 0.5 + x = 2
⇒ x = 1.5
Hence, the capacity of the capsule
= 2 × (Volume of the hemisphere) + (Volume of the cylinder)
`=(2xx2/3pi"r")^3+pi"r"^2"h"`
`=(4/3xx22/7xx1/4xx1/4)+(22/7xx1/4xx1/4xx1.5)` `["since" 0.25 =1/4] `
`=(11/168 + 33/112) "cm"^3`
`=121/336 "cm"^3 = 0.36 "cm"^3`
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