Question

How many liters of water will be contained in a hemispherical bowl whose radius is 2 meters? (1 liter = 1000 cubic cm.)

Answer 1

Hint: We will first mention the formula for volume of hemisphere and then we will put in the given data of radius as 2 meters and then calculate as required and get the answer.

Complete step-by-step solution:
We must note that the volume of a hemisphere is given by the formula mentioned in the following expression:-
$ \Rightarrow $ Volume of hemisphere = $\dfrac{2}{3} \times \pi {r^3}$, where r is the radius of the hemisphere.
Now, since we are given that the radius of the bowl is given to be 2 meters.
Let us convert it into cm so that we can later convert cm into liters by the given conversion:-
1 liter = 1000 cubic cm
$ \Rightarrow $1 meter = 100 cm.
$ \Rightarrow $2 meters = $\left( {2 \times 100} \right)cm$ = 200 cm.
$ \Rightarrow $ Volume of hemispherical bowl = $\dfrac{2}{3} \times \pi \times {\left( {200cm} \right)^3}$
We know that $\pi = \dfrac{{22}}{7}$
$\therefore $Volume of hemispherical bowl = $\left( {\dfrac{2}{3} \times \dfrac{{22}}{7} \times 8000000} \right)c{m^3}$
Since, we are given in the question that:-
$ \Rightarrow $1000 cubic cm = 1 liter
$ \Rightarrow $1 cubic cm = $\dfrac{1}{{1000}}liters$
$ \Rightarrow \left( {\dfrac{2}{3} \times \dfrac{{22}}{7} \times 8} \right)c{m^3} = \dfrac{{\dfrac{2}{3} \times \dfrac{{22}}{7} \times 8000000}}{{1000}}liters$
$ \Rightarrow \left( {\dfrac{2}{3} \times \dfrac{{22}}{7} \times 8} \right)c{m^3} = \left( {\dfrac{2}{3} \times \dfrac{{22}}{7} \times 8000} \right)liters$

This means approximately 16746.666… liters of water can be stored in the water.

Note: The students must note that they might make the mistake of forgetting to convert the meters into cm and they must convert them because in the end, they need to convert the cubic cm into liters to get the answer in liters. Since, we are not given the conversion from meters to liters, we need to convert into cm to get the required answer.
The students must commit to memory the following formula:-
$ \Rightarrow $ Volume of hemisphere = $\dfrac{2}{3} \times \pi {r^3}$, where r is the radius of the hemisphere.
The students must note that they may use any value of $\pi $, be it $\dfrac{{22}}{7}$ or 3.14 because in the question, there is no such specific value mentioned. But, if there is a value mentioned, we must use that only to get the exact answer.