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?
Posted by Sadhna Kashyap 8 years, 3 months ago
- 3 answers
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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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[144−25]=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
1Thank You