A medicine capsule is in the shape of a cylin | vedclass

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(C) Given,diameter of cylinder $=$ Diameter of hemisphere $= 0.5\, cm$ (since both hemispheres are attached to the cylinder).$	herefore$ Radius of cy

Vedclass · Accepted Answer

$0.36$

Vedclass · Answer

(C) Given,diameter of cylinder $=$ Diameter of hemisphere $= 0.5\, cm$ (since both hemispheres are attached to the cylinder).$	herefore$ Radius of cylinder $(r) =$ radius of hemisphere $(r) = \frac{0.5}{2} = 0.25\, cm$ (since diameter $= 2 	imes$ radius).Total length of capsule $= 2\, cm$.Length of the cylindrical part of the capsule $(h) = 	ext{Total length} - (	ext{Radius of left hemisphere} + 	ext{Radius of right hemisphere})$.$h = 2 - (0.25 + 0.25) = 2 - 0.5 = 1.5\, cm$.Now,capacity of the capsule $=$ Volume of cylindrical part $+ 2 	imes$ Volume of hemisphere.Capacity $= \pi r^2 h + 2 	imes (\frac{2}{3} \pi r^3) = \pi r^2 (h + \frac{4}{3} r)$.Substituting the values:Capacity $= \frac{22}{7} 	imes (0.25)^2 	imes (1.5 + \frac{4}{3} 	imes 0.25)$.Capacity $= \frac{22}{7} 	imes 0.0625 	imes (1.5 + 0.3333) = \frac{22}{7} 	imes 0.0625 	imes 1.8333 \approx 0.36\, cm^3$.Hence,the capacity of the capsule is $0.36\, cm^3$.

$A$ medicine capsule is in the shape of a cylinder of diameter $0.5\, cm$ with two hemispheres stuck to each of its ends. The length of the entire capsule is $2\, cm$. The capacity of the capsule is (in $cm^3$):

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