Saved Bookmarks
| 1. |
A well with inside diameter 10m is dug 8.4m deep. Earth taken out of it is spread all around it to a width of 7.5m to form an embankment. Find the height of the embankment. |
|
Answer» The dimensions of the well are Radius = 5m Depth = 8.4m We know that Volume of the earth dug out = Volume of well = πr2h By substituting the values Volume of the earth dug out = (22/7) × (5)2 × 8.4 So we get Volume of the earth dug out = 660 m2 It is given that Width of embankment = 7.5m We know that External radius of embankment R = 5 + 7.5 = 12.5m Internal radius of embankment r = 5m We know that Area of embankment = π (R2 – r2) By substituting the values Area of embankment = (22/7) × (12.52 – 52) On further calculation Area of embankment = (22/7) × (156.25 – 25) So we get Area of embankment = (22/7) × 131.25 = 412.5 m2 We know that Volume of embankment = volume of earth dug out = 660m2 So the height of embankment = volume of embankment/ area of embankment By substituting the values Height of embankment = 660/ 412.5 = 1.6m Therefore, the height of the embankment is 1.6m. |
|