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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. - CBSE Class 10 - Mathematics

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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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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 13: Surface Areas and Volumes
Ex. 13.30 | Q: 3 | Page no. 251

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Solution 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. Concept: Conversion of Solid from One Shape to Another.
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