a well of radius 7 m is dug to a depth of 12 m earth taken out of it has been evenly spread all around to form a circular embankment of width 7 m find the height of the embankment?
Please answer in proper steps
Answers
Answer:
4 m
Step-by-step explanation:
Given,Radius of the well (r) = 7 m.
Height of the well = 12 m.
∴ Volume of the earth taken out of the well = πr²h
= (22/7) * (7)² * 12
= 1848 m³
Given that It has been evenly spread of width 7 m.
Outer radius of the embankment = 14 m.
Now,
Area of embankment = πR² - πr²
= π(R² - r²)
= (22/7)[14² - 7²]
= (22/7)[147]
= 462 m²
∴ Height of the embankment = 1848/462
= 4 m.
Therefore, Height of embankment = 4 m.
Hope it helps!
GIVEN width of embankment = 7mts
its inner radius (r) = 7 ms and outer radius (R) = 7+7=14mts
volume of earth dug out = vol of soil in embankment
πr²h = vol of soil in embankment
22/7×7²×12000 = π h ( R²- r² )
1848000 = 22/7 × h × ( 14²-7² )
1848000 × 7/22 = h x 147
h = 84000 x 7 / 147
h = 588000 / 147
h = 4000 mts