3 Tutor System
Starting just at 265/hour

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.

Let $$h$$ be the required height of the platform.

The shape of the platform will be like the shape of a cuboid of dimensions $$22 \ m \ × \ 14 \ m \ × \ h$$ with a hole in the shape of cylinder of radius $$3.5 m$$ and depth $$h$$.

The volume of the platform will be equal to the volume of the earth dug out from the well.

Now, the volume of the earth = Volume of the cylindrical well

$$= \ \pi r^2 h \ = \ \frac{22}{7} \ × \ 12.25 \ × \ 20 \ = \ 770$$ m3

Also, the volume of the platform $$= \ 22 \ × \ 14 \ × \ h$$ m3

But volume of the platform = Volume of the well

$$\Rightarrow \ 22 \ × \ 14 \ × \ h \ = \ 770$$

$$\Rightarrow \ h \ = \ \frac{770}{22 \ × \ 14} \ = \ 2.5$$ m

$$\therefore$$ Height of the platform = 2.5 m