Question

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? 

Answer 1

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)

As all the rain water is transferred to the cylindrical vessel

We can equate 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.