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A medicine-capsule is in the shape of a cylinder of diameter $0.5 cm$ with two hemispheres stuck to each to its ends. The length of entire capsule is $2 cm$ . The capacity of the capsule is

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{0.36 cm}^{3}

{0.35 cm}^{3}

{0.34 cm}^{3}

{0.33 cm}^{3}

answer is A.

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Detailed Solution

It is given medicine-capsule is in the shape of a cylinder of diameter

0.5 cm

with two hemispheres stuck to each to its ends and length of entire capsule is

2 cm

.
Let r be radius and h be length of entire capsule.
Question Image

Capsule consists of 2 Hemispheres and a Cylinder (as shown in figure below),
Now,

r = \frac{0.5}{2} cm

\Rightarrow r = 0.25 cm

Total length of capsule =

r + h + r

\Rightarrow 2 cm = 2 r + h

\Rightarrow 2 = 2 \times 0.25 + h

\Rightarrow h = 2 - 0.5

\Rightarrow h = 1.5 cm

Volume of capsule = Volume of two hemispheres + Volume of cylinder

\Rightarrow 2 \times (\frac{4}{3} π r^{3} \times \frac{1}{2}) + π r^{2} h = \frac{4}{3} π r^{3} + π r^{2} h

\Rightarrow π r^{2} [\frac{4}{3} r + h] = \frac{22}{7} \times 0.25 \times 0.25 [\frac{4}{3} \times 0.25 + \frac{15}{10}]

\Rightarrow \frac{22}{7} \times 0.25 \times 0.25 [\frac{4}{3} \times \frac{25}{100} + \frac{3}{2}]

\Rightarrow \frac{22}{7} \times 0.25 \times 0.25 [\frac{1}{3} + \frac{3}{2}]

\Rightarrow \frac{22}{7} \times 0.25 \times 0.25 [\frac{2 + 9}{6}]

\Rightarrow \frac{22 \times 25 \times 25 \times 11}{7 \times 6 \times 100 \times 100}

\Rightarrow \frac{121}{42 \times 8}

\Rightarrow \frac{121}{336}

\Rightarrow {0.36 cm}^{3}

Therefore, volume of capsule

= {0.36 cm}^{3}

Hence, the correct option is 1.

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