Question

Circumference of the edge of the hemispherical bowl is 132cm. Find the capacity of the bowl.

Answer 1

Hint: In this question use the direct formula for circumference of the edge of the hemisphere which is given as $\left( {2\pi r} \right)$. The capacity refers to the volume of the hemisphere which is given as $\left( {\dfrac{2}{3}\pi {r^3}} \right)$.

Complete step-by-step answer:

Consider the hemispherical bowl as shown above.
Let the radius of the hemispherical bowl be r cm.
As we know that the top part of hemispherical bowl is a circle whose circumference is given as $\left( {2\pi r} \right)$ where r is the radius of the bowl.
Now it is given that the circumference of the bowl is 132 cm.
$ \Rightarrow 2\pi r = 132$
$ \Rightarrow r = \dfrac{{132}}{{2\pi }}$ cm.
Now we have to find the capacity of the bowl.

As we know, the capacity of the bowl is nothing but the volume of the bowl.
Now as we know that the volume (V) of the hemispherical bowl is $\left( {\dfrac{2}{3}\pi {r^3}} \right)$ cubic units.
 $ \Rightarrow V = \dfrac{2}{3}\pi {{\text{r}}^3}{\text{c}}{{\text{m}}^3}$
Now substitute the value of r we have,
$ \Rightarrow V = \dfrac{2}{3}\pi {\left( {\dfrac{{132}}{{2\pi }}} \right)^3}{\text{ c}}{{\text{m}}^3}$
Now simplify the above equation we have,
$ \Rightarrow V = \dfrac{1}{3}\dfrac{{{{\left( {132} \right)}^3}}}{{4{\pi ^2}}} = \dfrac{1}{3}\dfrac{{{{\left( {132} \right)}^3}}}{{4 \times \dfrac{{22}}{7}}} = \dfrac{{132 \times 132 \times 132 \times 7}}{{4 \times 22 \times 3}} = {\text{ 60984c}}{{\text{m}}^3}$
So this is the required capacity of the hemispherical bowl.

Note: It is always advised to remember the basic formula for volume, circumference for shapes like cuboid, sphere etc. Hemisphere as the name suggests is the half of sphere thus most of the formula applicable on sphere can easily be used in case of hemisphere by just doing them into half.