Question

Assume
`\pi=(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

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

Step-by-step 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)) = (22)/(7) * {(3.5)}^(2) * 4 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf Volume_((Cylinder)) = (22)/(7) * 12.25 * 4 \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf Volume_((Cylinder)) = \frac{22}{ \cancel{7} } *{ \cancel{ 49}} \\ \\ \\ \: \: \: \: \dashrightarrow \: \: \: \: \sf Volume_((Cylinder)) = 22 * 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 * 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.