Q. 144.0( 4 Votes )

# 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 cm^{3}

B. 0.35 cm^{3}

C. 0.34 cm^{3}

D. 0.33 cm^{3}

Answer :

Capacity of capsule = Volume of 2 hemispherical part + volume of cylindrical part

Now,

Diameter of capsule = 0.5 cm

Radius of capsule, r = 0.25 cm

[as radius = 1/2 diameter]

Also,

Radius of hemispherical part = Radius of cylindrical part = r

Height of entire capsule = 2 cm

Let the height of cylindrical part be h.

Then

Height of entire capsule = radius of 2 hemispherical parts + height of cylindrical part

⇒ 2 = 2r + h

⇒ 2 = 2(0.25) + h

⇒ h = 1.5 cm

Volume of capsule

Volume of hemisphere of radius, r = (2/3) πr^{3}

And volume of cylinder = πr^{2}h,

where r = base radius,

h = height of cylinder

Volume of capsule

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