Question

A well with 6 m diameter is dug. The earth taken out of it is spread uniformly all around it to a width of 2 m to form an embankment of height 2.25 m. Find the depth of the well.

Answer 1

Radius of the well (r)

= `(6)/(2)`
= 3m
Volume of earth dug out of the well
= πr²h  ...(Volume of cylinder)
= π x (3)² x h
= 9πh m²
Area of embankment = πR² - πr²
Where R = r + width of the embankment
= 3 + 2
R = 5m
Area of embankment
= π5² -π3²
= 16π m²
Volume of earth dug out for the embankment
= area of embankment x height
9πh = 16π x 2.25

h = `(16π xx 2.25)/(9π)`
∴ h = 4m
∴ The depth of the well is 4m.