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 = πr^{2}h

⇒ volume of well dug = × × 20

= × × 20

= 22 × 7 × 5

= 770 m^{3}

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 m^{3}

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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