Question

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 1

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.