Question

Assume $\pi=\frac{22}{7},$ unless stated otherwise.
8. A patient in a hospital is given soup daily in a cylindrical bowl of diameter $7 \mathrm{~cm}$ . If the bowl is filled with soup to a height of $4 \mathrm{~cm}$ , how much soup the hospital has to prepare daily to serve 250 patients?

Answer 1

Answer:

• 38.5 litres soup the hospital has to prepare daily to serve 250 patients.

Step-by-step explanation:

As we given that A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm.

So,

• Heigth of cylinder = 4 cm
• Diameter of cylinder = 7 cm
• Radius of cylinder = 7/2 = 3.5 cm

$\bigstar$To Find Volume of soaps required in the hospital to prepare daily to serve 250 patients. Firstly we need to find The volume of Soap in each bowl for 1 patient.

Using formula:

$\\ \: \: \: \: \dashrightarrow \: \: \: \: \sf \red{\underbrace{Volume_{(Cylinder)} = \pi r^2 h}}$

On substituting the required values, we get:

$\\ \: \: \: \: \dashrightarrow \: \: \: \: \sf Volume_{(Cylinder)} = \dfrac{22}{7} \times {(3.5)}^{2} \times 4 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf Volume_{(Cylinder)} = \frac{22}{7} \times 12.25 \times 4 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf Volume_{(Cylinder)} = \frac{22}{ \cancel{7} } \times{ \cancel{ 49}} \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf Volume_{(Cylinder)} = 22 \times 7 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf{ \red{ \underbrace{Volume_{(Cylinder)} = 154 \: {cm}^{3}}}}$

Hence, We have get the volume of soap for 1 patient is 154 cm³.

Now we need to find the volume of soap for 250 patients:

$\\ \: \: \: \: \: \: \dashrightarrow \: \: \: \: \: \: \sf 154 \times 250 \\ \\ \: \: \: \: \: \dashrightarrow \: \: \: \: \: {\red{\underbrace {\sf {38500 \: cm^3}}}}$

Soap In litres:

• 1000 cm³ = 1 litre
• 38500/1000 = 38.5 litres

$\therefore$38.5 litres soup the hospital has to prepare daily to serve 250 patients.