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If the circumference of the inner edge of a hemispherical bowl is $\frac{132}{7}$ cm, then what is the capacity?

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12 πc m^{3}

18 πc m^{3}

24 πc m^{3}

36 πc m^{3}

answer is B.

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Detailed Solution

Given the circumference of the inner edge of a hemispherical bowl is

\frac{132}{7}

cm.
The formula for the circumference of hemisphere is

2 πr,

where r is its radius.
Then,

2 πr = \frac{132}{7}

\Rightarrow r = \frac{132}{7} \times \frac{7}{44}

\Rightarrow r = 3

cm
The formula for the volume of sphere is given by,
Volume of sphere

= \frac{4}{3} π r^{3}

So, after substituting the value of all the dimensions in the formula we get,
Then capacity = volume of hemispherical

= \frac{2}{3} \times π (3)^{3}

= \frac{2}{3} \times 27 π

= 18 πc m^{3}

Therefore, the capacity of bowl is

18 πc m^{3} .

Hence option (2) is correct.

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