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Question 14
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 entire capsule is 2 cm. the capacity of the capsule is
(A) 0.36 cm3
(B) 0.35 cm3
(C) 0.34 cm3
(D) 0.33 cm3

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Solution

Given, diameter of cylinder = diameter of hemisphere = 0.5 cm
[since , both hemispheres are attach with cylinder]
Radius of cylinder (r) = radius of hemisphere (r)=0.52=0.25 cm[diameter=2×radius]

And total length of capsule = 2 cm.
Length of cylindrical part of capsule.
h = Length of capsule – Radius of both hemispheres

Now, capacity of capsule
= Volume of cylindrical part +2× Volume of hemisphere
=πr2h+2×23πr3
[Volume of cylinder=π×(radius)2×height and volume of hemisphere=23π(radius)3=227[(0.25)2×1.5+43×(0.25)3]=227[0.09375+0.0208]=227×0.11455=0.36 cm3(approx)

Hence, the capacity of capsule is 0.36 cm3

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