Question

A $20m$ deep well with a diameter of $7m$ is dug and the earth from digging is evenly spread out to form a platform$22mby14m.$ Find the height of the platform.

Answer 1

Step 1: Given Information

Diameter of cylinder = $7m$

So, Radius of cylinder (r)= $\frac{diameter}{2}=\frac{7}{2}=$$3.5m$

Height of cylinder (h)= $20m$

Length of platform (Cuboidal shape) (l) = $22m$

Breadth of Platform (Cuboidal shape) (b) =$14m$

Step-2: Find the amount of digging

Amount of digging$=\text{volume of well ( cylindrical in shape )}$

$={\mathrm{\pi r}}^2\mathrm{h}$ ( As Volume of cylinder= ${\mathrm{\pi r}}^2\mathrm{h}$)

$=\frac{22}{7}\times 3.5\times 3.5\times 20$

$=22\times 0.5\times 3.5\times 20$ ( As $\frac{3.5}{7}=0.5$)

$=22\times 0.5\times 70$ (As $20\times 3.5=70$)

$=22\times 35m$

Step-3: Find the height of the platform (cuboidal shape) i.e. $h$

Dimension of platform = amount of digging

or, Volume of platform = amount of digging

$l\times b\times h=$Amount of digging ( As Volume of cuboidal platform = $l\times b\times h$ )

$l\times b\times h=22\times 35$ ( As the amount of digging $22\times 35m$)

$22\times 14\times h=22\times 35$

$\Rightarrow$$h=\frac{22\times 35}{22\times 14}$( Transposing $22\times 14$from left side to right side and while doing so multiplication becomes division )

$\Rightarrow$$h=\frac{35}{14}$ (Simplify $\frac{35}{14}$by dividing by a common factor $7$in Numerator and Denominator separately )

$\Rightarrow$$h=\frac{5}{2}m$

$\Rightarrow$$h=2.5m$

Hence, the height of the platform is $2.5m$.