# A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment

**Solution:**

Given: Depth of the well is 14 m and diameter is 3m. Width of the circular ring of the embankment is 4 m.

Reasoning:

A figure is drawn below to visualize the shapes.

From the above figure, we can observe that the shape of the well will be cylindrical, and earth evenly spread out to form an embankment around the well in a circular ring will be in a cylindrical shape (Hollow cylinder) having outer and inner radius.

Volume of the earth taken out from well = Volume of the earth used to form embankment

Hence, Volume of the cylindrical well = Volume of the hollow cylindrical embankment

Let us find the volume of the hollow cylindrical embankment by subtracting volume of inner cylinder from volume of the outer cylinder.

Volume of the cylinder = πr²h

where r and h are the radius and height of the cylinder respectively.

Depth of the cylindrical well, = h_{1} = 14 m

Radius of the cylindrical well, = r = 3/2 m = 1.5 m

Width of embankment = 20 m

Inner radius of the embankment, r = 3/2 m

Outer radius of the embankment, R = Inner radius + Width

R = 1.5 m + 4 m

= 5.5 m

Let the height of embankment be h

Volume of the cylindrical well = Volume of the hollow cylindrical embankment

πr²h_{1} = πRh + πr²h

πr²h_{1} = πh (R² + r²)

r²h_{1} = h (R - r )(R + r)

h = [(r²h_{1})/(R - r)(R + r)]

h = [((1.5 m)² × 14 m)/(5.5 m - 1.5 m)(5.5 m + 1.5 m)]

= 2.25 m² × 14 m)/(4m × 7 m)

= 1.125m

Therefore, the height of the embankment will be 1.125 m.

**Video Solution:**

## A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment

### NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.3 Question 4 - Chapter 13 Exercise 13.3 Question 4 :

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment

The height of the embankment formed by digging a well of diameter 3 m and and depth of 14 m is 1.125 m