9. A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in
her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the sea
rate of 3 km/h, in how much time will the tank be filled?
one 4
Fig. 13
13.5 Frustum of a Cone
Answers
Step-by-step explanation:
Given :
Internal diameter = 20 cm
Flowing rate = 3km/hr
Solutions : Let the Cylindrical tank filled be X hr
Length of water column In X hr = 3x km
= 3x × 1000 m
= 3000x m
Remark : 1 km = 1000m
So convert 3x km to m
Radius of pipe = 20/2
Radius of pipe = 10 cm
Remark 1 cm = 100m
so convert 10 cm to m
Divided by 100 to 10
10 cm = 10 m / 100
= 1/10m
Radius Of pipe = 1/10 m
According to formula Cylindrical πr^2h
Volume of the water flowing in pipe X hr = π r^2h
= π ( 1/10 ) ^2 × 3000x
= π ( 1/100 ) × 3000x ( divide 100 by 3000)
= 30πxm^3
Diameter of Cylindrical tank = 10m
Height = 2m
Radius of Cylindrical tank = 10/2
= 5m
Volume of water in flowing pipe X hr = Volume of tank
30πx = 50π ( cancelled π to π )
30x = 50
X = 50/30
X = 5/3 hr
X = 1 right 2/3
So convert 5/3 to HR and min
2/3×60 = 40 min
X = 1 hr 40 min
Tank filled In 1 hr 40 minutes