Answer :
area of cross section of cylindrical pipe = π/16 cm^2. therefore volume of water flowing through the pipe per minute = π/16*10*100 cm^3 = 125π/2 cm^3. volume of cone = 1/3*π*400*24 = 3200π cm^3. therefore time taken to fill the cone = 3200π*2/125π = 6400/125 = 51.2 minutes.
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