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Question

A 20 m deep well of diameter 7 m is dug and the earth taken out is evenly spread out to form a platform of 22 m by 14 m. Find the height of the platform.


A

5 m

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B

10 m

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C

2.5 m

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D

7.5 m

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Solution

The correct option is C

2.5 m


Given:
Diameter of the well, d = 7 m
Radius of the well, r = 72 = 3.5 m
Height of the well, h = 20 m
Length of the platform, 1 = 22 m
Breadth of the platform, b = 14 m

Let height of the platform be h1.

Well is in the shape of a cylinder.
Volume of cylinder is given by πr2h.
Platform is in the shape of a cuboid.
Volume of cuboid is given by 'length × breadth × height'.

According to given condition we have:
Volume of the well = Volume of the platform
πr2h=l×b×h1

227×3.5×3.5×20=22×14×h1

h1=227×3.5×3.5×2022×14

h1=2.5 m


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