Question

Water flows at the rate of0.5m/minthrough a cylindrical pipe, whose internal radius is2cm. How long would it take to fill a conical vessel whose base radius is10cmand depth is30cm?

Answer 1

Answer:

Time taken = 5 mins

Step-by-step explanation:

Given:

• Water flows at the rate of 0.5m/min
• Internal radius of the pipe = 2 cm
• Radius of the conical vessel = 10 cm
• Depth of the conical vessel = 30 cm

To Find:

• Time taken to fill the conical vessel

Solution:

First find the volume of water that flows out through the pipe in 1 min.

Here the pipe is in the shape of a cylinder.

Volume of a cylinder is given by,

Volume of a cylinder = π × r² × h

where r is the radius

and h is the height

Here height of the pipe = 0.5 m = 50 cm

Substitute the data,

Volume of water that flows out in 1 min = π × 2² × 50

⇒ 200 π cm³

Now the vessel is in the shape of a cone.

Volume of a cone is given by,

Volume of a cone = 1/3 × π × r² × h

Substitute the given data,

Volume of the cone = 1/3 × π × 10² × 30

Volume of the cone = 1000 π cm³

Now let the conical vessel be filled in x mins.

Hence,

Volume of water that flows out in x mins = Volume of the vessel

Substitute the data,

200 π × x = 1000 π

200 x = 1000

x = 1000/200

x = 5 mins

Hence the time taken to fill the conical vessel is 5 mins.

Answer 2

■ Question :-

➢ Water flows at the rate of0.5m/min through a cylindrical pipe, whose internal radius is2cm. How long would it take to fill a conical vessel whose base radius is10cmand depth is30cm?

■ Given :-

➤ Water flows at the rate of0.5m/min

➤ A cylindrical pipe

➤ Radius of pipe is 2 cm .

➤ A conical vessels whose radius and depth is 10 cm and 30 cm respectively.

■ To find :-

➣ We have to find time taken to fill the conical vessels.

■ SolutiOn :-

We have to find the volume of water which flows in 1 min .

we know that ,

The shape of pipe is cylindrical so, The formula of volume of cylinder as follows :-

V = πr²h

After putting the values ,

= 22/7 × 2² × 50

= 22/7 × 200 --------------(1)

Now ,

we have to find the volume of cone because vessels is in the shape of cone,

Formula :-

V = 1/3×πr²h

After putting the values,

= 1/3 × 22/7 × 10² × 30

= 22/7 × 100 × 10

= 22/7 × 1000 -----------------(2)

Now ,

Let the time taken to filled be x minutes .

Hence,

Equation 1 × x = Equation 2

so,

200 × 22/7 × x = 1000 × 22/ 7

therefore , 200x = 1000

x = 1000/200

x = 5 minutes

Hope it's helpful