# A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform

**Solution:**

A figure is drawn below to visualize the shapes.

The shape of the well will be cylindrical, and soil evenly spread out to form a platform will be in a cuboidal shape.

So, the volume of the soil dug from the well will be equal to the volume of soil evenly spread out to form a platform.

Volume of soil dug out from the well = Volume of soil used to make such platform

Hence, Volume of the cylindrical well = Volume of the cuboidal platform.

We will find the volume of the cylinder and cuboid by using formulae;

Volume of the cylinder = πr^{2}h, where r and h are the radius and height of the cylinder respectively.

Volume of the cuboid = l × b × H, where l, b, and H are length breadth and height of the cuboid respectively.

Depth of the cylindrical well, h = 20 m

Radius of the cylindrical well, r = 7/2 m

Length of the cuboidal platform, l = 22 m

Breadth of the cuboidal platform, b = 14 m

Let the height of the cuboidal platform = H

Volume of the cylindrical well = Volume of the cuboidal platform

πr^{2}h = lbH

H = lb / πr^{2}h

= (22/7 × 7/2 m × 7/2 m × 20 m) / (22 m × 14 m)

= 5/2 m

= 2.5 m

Therefore, the height of platform will be 2.5 m.

**Video Solution:**

## A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform

### NCERT Solutions for Class 10 Maths - Chapter 13 Exercise 13.3 Question 3 :

A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform

The height of the platform formed by digging a 20 m deep well having diameter 7 m is 2.5 m