A well is dug with 14 m diameter
and a depth of 10 m. The earth taken out is
spread evenly on a plot of land 100 m long and
7 m wide. Find the height of the platform thus
formed by the earth.
Answers
Question :-
→ A well is dug with 14 m diameter
and a depth of 10 m. The earth taken out is
spread evenly on a plot of land 100 m long and
7 m wide. Find the height of the platform thus
formed by the earth.
Given :-
→ Inner Diameter of the well= 14 m
→ Inner Radius of the well (r) = 14/2 m = 7 m
→ Height of the well (h) = 15 m
→ Width = 7m
Solution :-
→ Volume of the earth taken out of the well = πr²h
= 22 × 7 × 15= 2310 m³
→ Outer radius of the embankment ( R )
=inner radius + width
→ Outer radius ( R ) = 7 + 7 = 14m
→ The embankment is in the form of cylindrical shell, so area of embankment
→ Area of embankment = outer area - inner area
= πR² - πr² = π(R²-r²)
= (22/7) ( 14² - 7²)
= 22/7(196-49)
= 22/7 × 147
= 22 × 21
= 462 m²
→ Volume of embankment
= volume of earth taken out on digging the well
→ Area of embankment × height of embankment= volume of earth dug out
→ Height of embankment= volume of earth dug out ÷ area of the embankment
→ Height of the embankment = 2310 ÷ 462
→ Height of embankment = 5 m