A well with 10m indie diameter is dug 8.4m deep. Earth taken out it is spread all around it to a width of 7.5m to form an embankment. Find the height of the embankment.
Urgently I need it
Answers
Answer
- Height of the embankment is 6.72 m
Explanation
Given
- Diameter of well = 10 m
- Depth/Height of well = 8.4 m
- Width of embankment = 7.5 m
To Find
- Height of embankment
Solution
First we have to find the volume of the cylindrical well
Volume of a cylinder is given by,
➝ Volume of a cylinder = π r² h
Substitute the values,
➝ Volume of cylinder = 3.14 × 10/2 × 10/2 × 8.4
➝ Volume of well = 3.14 × 5 × 5 × 8.4
➝ Volume of the well = 659.4 m³
Now,
★ Volume of well = Volume of the earth taken out
So the then,
➝ Volume of earth taken out = 659.4 m³
Volume of Embankment
➝ Volume of embankment = Volume of outer cylinder - Volume of inner cylinder
➝ Volume of embankment = π R² h - π r² h
[Taking πh as common]
➝ Volume of embankment = πh (R² - r²)
➝ Volume of embankment = 3.14 h (7.5² - 5²)
➝ Volume of embankment = 3.14 × 31.25 h
➝ Volume of embankment = 98.125 h
Height of Embankment
★ Volume of embankment = Volume of Earth taken out = Volume of the well
➝ 659.4 = 98.125 h
➝ 659.4/98.125 = h
➝ Height = 6.72 m