Question

If the circumference of the edge of a hemisphere bowl is 132 cm. Then find the capacity of the bowl.

Answer 1

Hint: Here we have to only find the radius of the bowl by comparing the given circumference of the edge with the formula \[2\pi r\] and then find the volume of bowl using the formula \[\dfrac{2}{3}\pi {r^3}\].

Complete step-by-step answer:

Now we are given the circumference of the edge of the hemispherical bowl and we know that the edge of the hemisphere is of the shape of a circle.

So, the formula for the circumference of the edge of the bowl will be \[2\pi r\]
So, according to question,
\[2\pi r\] = 132
On dividing both sides of the above equation by \[2\pi \]. We get,
\[r = \dfrac{{132}}{{2\pi }} = \dfrac{{132 \times 7}}{{2 \times 22}} = \dfrac{{42}}{2} = 21\]cm
So, now as we know that we are asked to find the capacity of the bowl and to find the capacity we first have to find the volume of the bowl in \[{m^3}\] or \[c{m^3}\]. And then change the unit to litres or millilitres to get the capacity of the bowl.
So, now as we know that the formula for volume of the hemisphere is \[\dfrac{2}{3}\pi {r^3}\].
So, volume = \[\dfrac{2}{3}\pi {\left( {21} \right)^3} = \dfrac{2}{3} \times \dfrac{{22}}{7} \times 21 \times 21 \times 21 = 19404{\text{ }}c{m^3}\]
So, now the capacity of the bowl will be equal to the maximum amount of water it can hold in litres.
So, now we had to change the volume from \[c{m^3}\] to millilitres.
As we know that the bowl with volume 1\[c{m^3}\] can hold a capacity of 1 millilitres of water.
So, 19404\[c{m^3}\] of the volume of the bowl will have a capacity of 19404 millilitres.
And as we know that 1 litre = 1000 millilitres.
So, 1 millilitre = \[\dfrac{1}{{1000}}\]litres
And, 19404 ml = \[19404 \times \dfrac{1}{{1000}} = 19.404\]litres
Hence, the capacity of the bowl will be 19.404 litres.

Note: Whenever we come up with this type of problem, we should remember that the capacity of a container does not depend on its shape; it is only dependent on the volume of that container. So, to find the capacity of any container first, we had to find the volume of that container (here bowl) we had to change its unit of volume i.e. \[c{m^3}\] to the required unit of capacity i.e. litres here. So, we can change the unit by using a unit conversion method like 1\[c{m^3}\] = 1 ml and 1 litre = 1000 ml.