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 the entire capsule is 2 cm. The capacity of the capsule is ______.

Options

• 0.33 cm³

• 0.34 cm³

• 0.35 cm³

• 0.36 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 the entire capsule is 2 cm. The capacity of the capsule is 0.36 cm³.

Explanation:

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`