Math, asked by BrainlyHelper, 1 year ago

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

Answered by nikitasingh79
15

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.

HOPE THIS ANSWER WILL HELP YOU….

Answered by BrainlyVirat
14

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.)

Similar questions