Question

A cylindrical shaped well of depth 20m and diameter 14m is dug. The dug out soil is evenly spread to form a cuboid-platform with base dimensions $ 20m \times 14m $ . Find the height of the platform.

Answer 1

Hint: A well in cylindrical shape is dug and the dugout soil is spread over the cuboid platform. So, the volume of the cylinder must be equal to the volume of the cuboid. So, first of all we will find the volume of the cylinder and then compare it with the volume of the cuboid to find its height.
 $ \Rightarrow $ Volume of cylinder $ \left( V \right) = \pi {r^2}h $
 $ \Rightarrow $ Volume of cuboid $ = l \times b \times H $

Complete step by step solution:
Given data:
Height of cylinder $ \left( h \right) = 20m $
Diameter of cylinder $ \left( d \right) = 14m $
Now, diameter $ \left( d \right) = 2r $
 $
  r = \dfrac{d}{2} \\
  r = \dfrac{{14}}{2} \\
  r = 7m \;
  $
Length of Cuboid $ \left( l \right) = 20m $
Breadth of Cuboid $ \left( b \right) = 14m $
Height of Cuboid $ \left( H \right) = ? $
Now, in the question it’s said that a cylindrical well is dug and its dug out soil is spread over a cuboid platform.
So, first of all let us find the volume of this dug out soil, which will be equal to the volume of the cylinder.
Now, volume of cylinder is given by below formula
 $ $ Volume $ \left( V \right) = \pi {r^2}h $
Where, $ r = $ radius of the cylinder
 $ h = $ Height of the cylinder
 $ \pi = \dfrac{{22}}{7} $
 $
   \Rightarrow V = \dfrac{{22}}{7} \times {7^2} \times 20 \\
   \Rightarrow V = 22 \times 7 \times 20 \\
   \Rightarrow V = 3080{m^3} \\
  $
Now, it is said that this dug out soil is spread over the cuboid platform.
So, the volume of this dug out soil that is the volume of the cylinder must be equal to the cuboid platform.
Therefore, $ $ Volume of Cylinder = Volume of Cuboid
Volume of cuboid $ = l \times b \times H $
 $ l = $ Length of cuboid
 $ b = $ Breadth of cuboid
 $ H = $ Height of cuboid
 $
   \Rightarrow 3080 = 20 \times 14 \times H \\
   \Rightarrow H = \dfrac{{3080}}{{20 \times 14}} \\
   \Rightarrow H = 11m \;
    $
Hence, the height of the cuboid platform is $ 11m $ .
So, the correct answer is “H = 11 m”.

Note: Units are most important while solving questions on area or volume. So, whenever solving questions on volume or area, cross check that you have mentioned the unit or the mentioned unit is correct or not. Also, sometimes dimensions are given in different units. So, make sure that you convert all the dimensions in the same unit before solving the question.