Question

A 16 m deep well with diameter 3.5 m is dug up and the earth from it is spread evenly to form a platform 27.5 m by 7 m. Find the height of the platform?

Answer 1

Let us assume the well to be a solid right circular cylinder

Radius(r) of the cylinder = 3.5/2 m = 1.75 m

Depth of the well or height of the cylinder (h) = 16 m

We know that,

Volume of the cylinder (V₁) = πr²h

= π × 1.75² × 16

Given,

The length of the platform (l) = 27.5 m

Breadth of the platform (b) =7 m

Now, let the height of the platform be x m

We know that,

Volume of the rectangle = l x b x h

V₂ = 27.5 x 7  x x

As the earth dug up is spread evenly to form the platform

Volumes of both, the well and the platform should be the same.

V₁ = V₂

π × 1.75 × 1.75 × 16 = 27.5 × 7 × x

x = 0.8 m = 80 cm

Therefore, the height of the platform is 80 cm.