Answer in Brief

A 16m deep well with diameter 3.5m is dug up and the earth from it is spread evenly to form a platform 27.5m by 7m. Find height of platform?

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#### Solution

Let as assume well is a solid right circular cylinder

us of cylinder(r) = 3.5/2 = 1.75m

Height (or) depth of well = 16m.

Volume of right circular cylinder = πr^{2}h

= `22/7` x (1.75)^{2 X 16 .............(1)}

Given that length of platform(l) = 27.5m

Breath of platform (b) = 7cm

Let height of platform be xm

Volume of rec tan gle = lbh

= 27.5 x 7 x `x`= 192.5`x` ..........(2)

Since well is spread evenly to form platform

So equating (1) and (2)

V_{1}_{ = }V_{2}

⇒` 22/7`(1.75)^{2 }x 16 = 192.5`x`

⇒ `x`= 0.8m

∴ Height of platform(h) = 80cm.

Concept: Volume of a Combination of Solids

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