Question

A well of inner diameter 14 m is dug to a depth of 12 m. Earth taken out of it has been evenly spread all around it to a width of 7 m to form an embankment. Find the height of the embankment so formed.

Answer 1

Given that, 

Inner diameter = 14 cm 

Therefore, 

Radius = 7 cm Also, Depth = 12 m 

Therefore,

Volume of earth dug out = πr²h

= \(\frac{22}{7}\times7\times7\times12\)

= 1848 m³ 

It is also given that, 

Width of embankment = 7 m 

Therefore, 

Total radius = 7 + 7 = 14 m 

Volume of embankment = Total volume – Inner volume 

= πr_o²h – πr₁²h 

= πh (r_o² – r₁²)

= \(\frac{22}{7}\)h (14² - 7²)

= \(\frac{22}{7}\)h x 147

= 21 × 22h 

= 462 × h m³ 

Since, 

Volume of embankment = Volume of earth dug out 

Therefore, 

1848 = 462 h

h = \(\frac{1848}{462}\)

h = 4 m 

Therefore, 

Height of the embankment = 4 m