can u please help me solve the following question Rain water which falls on a flat rectangular surface of - Maths - Surface Areas and Volumes

Question

can u please help me solve the following
question?
Rain water which falls on a flat rectangular
surface of length=6m and breadth=4m is transferred into a
cylindrical vessel of internal radius 20cm What will be the height
of water in the cylindrical vessel if the rain fall is 1cm give the
ans to the nearest whole no (use [pi] as 3
14)

Ajanta Trivedi · Accepted Answer

The length and breadth of the rectangular surface be 6m and 4m respectively.

the area of the rectangular surface = 6*4 = 24 sq m.= 240000 sq cm

the rain fall = 1 cm

the volume of water in rain fall = area*height(i.e. rainfall)=240000*1=240000 cubic cm.

the radius of the cylinder = 20 cm

area of the cross section of the cylinder = $π * 20^{2} = 400 π c m^{2}$

let the height of the water be h cm

the volume of the water in the cylinder = area of the cross section * height

$= 400 π h c m^{3}$

the volume of the water in rain fall = volume of the water in the cylinder

$240000 = 400 π h h = \frac{240000}{400 π} = \frac{600}{3.14} = 191.08 c m$

thus the height of the water in the cylinder is 191 cm.

hope this helps you