A well of inner diameter 14 m is dug to a depth of 12 m. Earth taken o

1.	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» 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

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»

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