Question

A patient in a hospital is given soup in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has prepared daily to serve 250 patients.

Answer 1

Hint –In this particular type of question use the concept that the amount given to every patient is the volume of the cylindrical bowl which is given as $\left( {V = \pi {r^2}h} \right)$, where symbols have their usual meaning so use this concept to reach the solution of the question.

Complete step-by-step answer:

Given data:
Soup is served in the hospital in a cylindrical bowl to every patient.
Height of the bowl (i.e. h) is = 4 cm
And the diameter of the bowl (i.e. D) = 7 cm
Now as we know that the radius (r) is half of the diameter (D) so we have,
$ \Rightarrow r = \dfrac{D}{2} = \dfrac{7}{2}$ cm.
Now the soup filled in the cylindrical bowl is equal to the volume of the cylindrical bowl.
Now as we know that the volume (V) of the cylindrical bowl = $\pi {r^2}h$, where r is the radius and h is the height of the bowl respectively.
So the volume of the bowl is,
$ \Rightarrow V = \dfrac{{22}}{7}{\left( {\dfrac{7}{2}} \right)^2}\left( 4 \right)$ Cubic centimeter.
Now simplify this we have,
$ \Rightarrow V = \dfrac{{22}}{7}{\left( {\dfrac{7}{2}} \right)^2}\left( 4 \right) = 154$ Cubic centimeter.
Now we have to calculate the amount of soup prepared by the hospital to serve 250 patients.
The amount of soup prepared is the product of the volume of the cylindrical bowl and the number of patients.
So, the amount of soup prepared is, A = $V \times 250$
Therefore, A = $154\left( {250} \right) = 38500$ cubic centimeter.
So this is the required answer.

Note – Whenever we face such types of questions the key concept we have to remember the volume of the cylinder which is stated above and also the radius of the cylinder is half the diameter, so first calculate the volume of the cylinder then multiply this volume by the number of patients we get the required amount of soup prepared by the hospital.