Q. 104.2( 16 Votes )

A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.

Answer :

The volume of earth removed by digging for cylindrical well is the same volume used to make platform which is cuboidal in shape


Therefore, volume of well dug = volume of platform formed


Parameters of well


Diameter = d = 7 m


radius = r = = m


The well is 20 m deep so we can say that its height is 20 m


Height = h = 20 m


Volume of cylinder = πr2h


volume of well dug = × × 20


= × × 20


= 22 × 7 × 5


= 770 m3


Parameters for platform


Length = l = 22 m


Breadth = b = 14 m


Let height be h


Volume of cuboid = l × b × h


Volume of platform = 22 × 14 × h


= 308h m3


As volume of well dug = volume of platform formed


770 = 308h


h =


Divide numerator and denominator by 7 we get


h =


Divide numerator and denominator by 22 we get


h = = 2.5


Therefore, height of platform is 2.5 m


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