# 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.

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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