Question

a 20 m deep pit with diameter 7m is dug up and the earth formed in is spread evenly to form a platform 22 metre * 14 M the height of the platform is

Answer 1

Heya!
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♦Surface Areas and Volumes ♦
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◾A 20m deep well with diameter 7m is dug up and the earth formed is spread evenly to form a platform 22m × 14m . Find the Height of the platform.


➰Here , we shall be using the concept that the volume of re casted shapes are equal .


Here ,


◾Volume of Well = Volume of the Platform


Given that =>
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Cylinder ( Well )
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Depth ( H ) of Well => 20 m

Diameter ( D ) = 7 m

Radius ( R ) = 7/2 m


Volume => πr²h

=> π × (7/2)² × 20..............(1)


For Platform =>
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Length = 22 m

Breadth = 14 m

Let Height be H


Volume = L × B × H

=> 14 × 22 × H ...............(2)



♦Putting (1) and (2) equal ,


=> 22/7 × 7/2 × 7/2 × 20 = 22 × 14 × H

=>> H = 2.5 m
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➰Hence the Height ( H ) of the platform is 2.5 m ✔

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Answer 2

Find the radius of the pit:

Radius = Diameter ÷ 2

Radius = 7 ÷ 2 = 3.5 m

Find the volume of the pit:

Volume = πr²h

Volume = π(3.5)²(20) = 770 m³

Find the height of the platform:

Volume = Length x Breadth x Height

770 = 22 x 14 x height

770 = 308 x height

Height = 770 ÷ 308 = 2.5 m

Answer: The height of the platform is 2.5m