Question

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 ______.

Options

• 0.36 cm³

• 0.35 cm³

• 0.34 cm³

• 0.33 cm³

Answer 1

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 0.36 cm³.

Explanation:

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)

= `0.5/2`

= 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

= 2 – (0.25 + 0.25)

= 1.5 cm

Now, capacity of capsule = Volume of cylinder part + 2 × Volume of hemisphere

= `pi"r"^2"h" + 2 xx 2/3 pi"r"^3`  ...[∵ Volume of cylinder = π × (radius)² × height and volume of hemisphere = `2/3` π(radius)³]

= `22/7 [(0.25)^2 xx 1.5 + 4/3 xx (0.25)^3]`

= `22/7 [0.09375 + 0.0208]`

= `22/7 xx 0.11455`

= 0.36 cm³

Hence, the capacity of capsule is 0.36 cm³.