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Question

A well with inner diameter 8 m is dug 14 m deep Earth taken out it has been spread evenly all around it to a width of 3 m to form an embankment around the well The height of this embankment is

A
62633 m
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B
72633 m
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C
42633 m
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D
52633 m
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Solution

The correct option is A 62633 m

Given Inner diameter of well =BC=8m

And Depth of well =14m

then volume of cylindrical well =πr2depth=π(BC2)2(depth)=π(BC2)(depth)4=π(82)(14)4=π(64)(14)4=224πm3

Let height of Embankment =xm

Diameter of outer cylindrical shape of Embankment =AD=AB+BC+CD=3+8+3=14m

then volume of Embankment =π(R2r2)height=π((outerdiameter)2(innerdiameter)2)x=π((AD2)2(BC2)2)x=πx4(AD2BC2)=πx4(14282)=πx4(19664)=132πx4=33πx

Now it says that well is dug deep Earth, taken out, and spread evenly all around to make Embankment.

So volume of Embankment would be same that of well.

Volume of Embankment = volume of well

33πx=224π

x=224π33π=22433=62633m

The height of this embankment is 62633m


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