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Question
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. [Use Π = 22/7]
Solution
The shape of the well will be cylindrical.
Depth (h) of well = 20 m
Radius (r) of circular end of well = 7/2 m
Area of platform = Length × Breadth = 22 × 14 m2
Let height of the platform = H
Volume of soil dug from the well will be equal to the volume of soil scattered on the platform.
Volume of soil from well = Volume of soil used to make such platform
Πxr2xh = Area of platform x Height of Platform
`Πxx(7/2)^2 xx 20 = 22xx14xxH`
`∴ H = 22/7xx 49/4xx20/(22xx14)= 5/2 m = 2.5 m`
Therefore, the height of such platform will be 2.5 m.
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