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?
Answers
Answer:
The height of the cylindrical vessel is 190.9 cm.
Step-by-step explanation:
Given :
Radius of the cylindrical vessel , r = 20 cm
Length of the rectangular surface , l = 6 m = 6 × 100 = 600 cm
[1 m = 100 cm]
Breadth of the rectangular surface , b = 4m = 4 × 100 = 400cm
Height of the rainfall, h = 1 cm
Volume of the rectangular surface = length × breadth × height = lbh
= 600 × 400 × 1 cm³
Volume of the rectangular surface = 240000 cm³ ……………… (1)
Let h cm be the height of the cylindrical vessel.
Volume of the cylindrical vessel = πr²h
= π× 20² × h………………………….(2)
Since rainfall is transferred into a cylindrical vessel, so volume of water in the cylindrical vessel is equal to the volume of rainfall (rectangular surface)
Volume of the rectangular surface = Volume of the cylindrical vessel
240000 cm³ = π× 20² × h
[ From eq 1 & 2 ]
240000 cm³ = 22/7 × 400 × h
h = (240000 × 7)/(22 × 400)
h =( 600 × 7)/22 = (300× 7)/11 = 2100/11
h =190.9 cm
Hence, The height of the cylindrical vessel is 190.9 cm.
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Let the length and breadth of the flat rectangular surface be 6m and 4m respectively.
Thus, the area of the rectangular surface = 6 × 4
= 24 sq m
= 240000 sq cm
Rain fall = 1 cm
The volume of water in rain fall = area × height (that is rainfall)
=240000*1
=240000 cu. cm.
Now,
radius of the cylinder = 20 cm
Area of the cross section of the cylinder = π × (20)^2
= 400 π cm^2
Now,
Let the height of the water be 'h' cm
Volume of the water in the cylinder = area of the cross section × height
= 400 π cm^3
Volume of the water in rain fall = volume of the water in the cylinder
Thus,
24000 cm^3= 400 π h cm^3
24000/400π = h
600/3.14 = h
191.08 = h
Thus, The height of the water in the cylinder is 191 cm. ( approx.)