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

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Very important question of mensuration including
very important concept of it.need solution!
Rd sharma class 10 maths exercise-16.1 mensuration.

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

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1. Let us assume the well to be a solid right circular cylinder

Radius(r) of the cylinder = 3.5/2 m = 1.75 m

Depth of the well or height of the cylinder (h) = 16 m

We know that,

Volume of the cylinder (V1) = Ï€r2h

= Ï€ Ã— 1.752 Ã— 16

Given,

The length of the platform (l) = 27.5 m

Breadth of the platform (b) =7 m

Now, let the height of the platform be x m

We know that,

Volume of the rectangle = l*b*h

V2 = 27.5*7*x

As the earth dug up is spread evenly to form the platform

Volumes of both, the well and the platform should be the same.

V1 = V2

Ï€ Ã— 1.75 Ã— 1.75 Ã— 16 = 27.5 Ã— 7 Ã— x

x = 0.8 m = 80 cm

Therefore, the height of the platform is 80 cm.

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