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?
Answers
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.
■ 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