Rain water, which falls on a flat rectangular surface of length 6 m and breadth 4 m is transferred into a cylindrical vessel of internal radius 20 cm. What will be the height of water in the cylindrical vessel if a rainfall of 1 cm has fallen?(Use π=22/7)
Answers
Answer:
Volume of water in rectangular flat=volume of cylindrical vessel
(6m)x (4m) x (1/100m)=pi. (r)^2.h
24/100m^3=(22/7)x (20/100m)^2.hm
24/100m^3= 88/700xh m^3
h=(21/11 )m
Step-by-step explanation:
Area of rectangle =6×4=24m²
Volume of water fallen on rectangular surface = Area×height
=24m²×0.01m
=0.24m³
This volume is transferred in cylindrical vessel of internal radius 0.2m.
Let height of water in vessel =h
So Volume of water =πr²h
=(22/7)(0.2)²h
this Volume of water = volume of water fallen on rectangular surface
=0.24m³
So
(22/7)(0.04)h=0.24
h=21/11
=1.9m
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Answer:-
Given:-
- Length of the rectangular surface = 6 m = 600 cm
- Breadth of the rectangular surface = 4 m = 400 cm
- Height of the perceived rain = 1 cm
So,
Volume of the rectangular surface = length × breadth × height
= 600 × 400 × 1 cm³
= 240000 cm³ → (i)
Also, given:-
Radius of the cylindrical vessel = 20 cm
Let the height of the cylindrical vessel be taken as h cm
We know that:-
Volume of the cylindrical vessel = π × r2 × h
= π × 20² × h → (ii)
Equating both (i) and (ii) for equal volumes,
240000 = π × 20² × h
h = 190.9 cm
Therefore, the height of the cylindrical vessel nearly 191 cm.