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Find the cub (cubical) volume of a hemisphere having diameter 1 cm.

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\frac{π}{6} c m^{3}

\frac{π}{12} c m^{3}

\frac{2 π}{3} c m^{3}

\frac{4 π}{3} c m^{3}

answer is B.

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Detailed Solution

Since the sphere is cut into half. Hence, its volume must also be halved.
Since the volume of a sphere is given by

V = \frac{4}{3 π r^{3}}

Hence, the volume of the hemisphere will be

V = \frac{1}{2} \times \frac{4}{3 π r^{3}} = \frac{2}{3} π r^{3}

V = \frac{2}{3} π r^{3}

………(1)
Now, we have a hemisphere of diameter 1 cm.

https://www.vedantu.com/question-sets/9499f240-4d11-4ed8-b4c6-3bce19929d283983725960351636159.png

We know that:

radius = \frac{diameter}{2}

So, the radius of the hemisphere will be

radius = \frac{1}{2} cm

.
Putting this value in (1) will result in:-

V = \frac{2}{3} π r^{3} = \frac{2}{3} π {(\frac{1}{2})}^{3}

\Rightarrow V = \frac{2}{3} \times π \times (\frac{1}{2}) \times (\frac{1}{2}) \times (\frac{1}{2}) {cm}^{3}

\Rightarrow V = \frac{1}{3} \times π \times \frac{1}{4} c m^{3} \Rightarrow V = \frac{π}{12} c m^{3}

Hence, the answer is

\frac{π}{12} c m^{3}

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