Question

Rain water falls on a flat rectangular surface of length 6m and breadth 4m is transfered into a cylindrical vessel of internal radius 20 cm . find the height of water in the cylindrical vessel if rain fall is 1cm.

Answer 1

ANSWER:

METHOD 1

Volume1=Volume2

600*400*1=22/7*20*20*h

h=600*7/22

h=4200/22

h=190.90cm

METHOD 2

Length of rectangular surface (L) = 6 m = 600 cm

Breadth of rectangular surface (B) = 4 m = 400 cm

Height of rectangular surface (H) = 1 cm

Radius of cylindrical vessel (r) = 20 cm

Let the height of cylindrical vessel = h cm

Volume of rectangular surface = Volume of cylindrical vessel

⇒ L × B × H

⇒ 600 × 400 × 1

⇒ h = 190.90 cm

∴ Height of the cylindrical vessel is 190.90 cm.

Answer 2

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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