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A well having 10m inside diameter …

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A well having 10m inside diameter is dug 8.4m deep.Earth taken out of it is spread all around it to a width of 7.0m to form a beautiful embankment. Find the height of embankment? The contractor charged Rs500 per cubic metre for digging and making the circular embankment. He measured height of the embankment as 2m. How much extra money he made?

  • 3 answers

Naveen Sharma 8 years, 3 months ago

Ans. Diameter of Well = 10 m

Radius of Well = 10/2 = 5m

Depth (height) of well = 8.4 m

Volume of Well = 227×(5)2×8.4=227×25×8.4

= 660 m3

Volume of Well = Volume of Earth Taken Out 

=> Volume of Earth Taken Out = 660m3 .....(1)

This earth spread around well, so it ll be in form of hollow cylinder.

Let Height of Embankment = h

Inner Radius  (r) = 5m

Width of Embankment (t) = 7 m

Outer Radius (R) = r + t = 5+7 =12 m

Volume of Embankment = Volume of outer cylinder - volume of inner cylinder

=> [227×(R)2×h][227×(r)2×h]

=> 227×h[14425]=227×h×119

=> 374h .........(2)

From (1) and (2)

=> 374h = 660

=> h = 1.765m

Rate For Digging And making embankment  = Rs. 500 per cubic meter

Actual Amount = 500 * [ Total Volume of Well + Volume Of embankment ] 

= 500*[660+660] = Rs. 660000

(as he consider height 2m)volume of embankment = 22*2*[144-25]/7= 44*119/7 = 748m3

Amount He Charged = 500* [ 660 +748 ]= 550*1408=774400

Extra money Made = 774400-660000 = Rs.114400

 

Sadhna Kashyap 8 years, 3 months ago

But madam my book answer is not match your answer.

Rashmi Bajpayee 8 years, 3 months ago

After digging and spreading the earth, we consider the shape of hollow cylinder.

Here, Radius of well = 5 m and Outer Radius of well = 5 + 7 = 12 

Let height of embankment be h meters.

Now, Volume of Earth spread = Volume of Well

π(12)2 × h = π(5)2 × 8.4

h = 25 × 8.4 ÷ 144 = 1.46 m

But charge taken by contractor for 2 m height = Rs.500

Actual charge for 1.46 m height = 500/2 × 1.46 = Rs.365

Contractor charged more by Rs.500 - Rs.365 = Rs.135.

 

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