Question

A well of diameter 14 metre is dug 28 deep. The Earth which is so dug out is spread evenly on a rectangular platform 44 metre long and 28 metre broad . Find the raised height of the platform.​

Answer 1

$\mathbf\blue{GIVEN \: :}$

• Depth of well = 28 m.
• Diameter, d = 14 m.
• Radius, r = $\dfrac {r}{2}$ = 7 m.

$\mathbf\orange{FORMULA \: :}$

• $\sf Diameter \: = \: \dfrac {Radius}{2}$
• $\sf Height \: of \: the \: cuboid \: = L \times B \times H$

$\mathbf\green{SOLUTION \: :}$

Volume of earth drug out = $\sf \pi r^{2}h$

=> $\sf \dfrac {22}{7} \times 7 \times 7 \times 14 m^{3}$

Let the height of the platform be ‘h’.

Volume of earth spread on rectangular platform,

=> $\sf Length \times breadth \times height$

=> $\sf 44 \times 28 \times h m^{3}$

=> $\sf \dfrac {22}{7} \times 7 \times 7 \times 28$

=> $\sf 44 \times 28 \times h$

=> $\sf \dfrac {22 \times 7 \times 28}{44 \times 28}$

=> $\sf \dfrac {7}{2} \: = \: h$

=> $\sf h \: = \: 3.5 \:m.$

$\therefore$ The height of the platform is 3.5 m.