Question

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

Answer 1

Hint: - Volume of earth will be always constant. That’s why the volume of wells will equal the volume of the platform. So when you compare both volumes you can find the height of the platform.
Volume of earth that has been dug out will be equal to the volume of the well.
Volume of well =$\pi {r^2}h$
Where radius is $\frac{{3.5}}{2}m$ and height is $16m$
That is volume of earth = $\pi \times \frac{{3.5}}{2} \times \frac{{3.5}}{2} \times 16$=$153.86{m^3}$
The earth which has been dug out has to be used to make the platform.
So, volume of platform=volume of earth
Platform is in the shape of cuboid so we use
Volume of cuboid ${\text{L}} \times {\text{B}} \times {\text{H}}$
$ \Rightarrow 27.5m \times 7m \times H = 153.86{m^3}$
$ \Rightarrow H = 0.799m$
Hence, height of the platform is $0.799m$
Note: -First you have to find how much volume of earth is taken out and compare that volume with the volume of platform .Volume of platform will be the same as volume of cuboid ,Because platform is in the shape of cuboid.