Question

In the middle of a rectangular field measuring 30m × 20m, a well of 7 m diameter and 10 m depth is dug. The earth so removed is evenly spread over the remaining part of the field. Find the height through which the level of the field is raised.

Answer 1

Let r m be the radius and h m be the depth of the well that is dug.
Volume of the well = $\mathrm{\pi }$​r²h = 22 × (3.5 m)² × (10 m) = 385 m³
7
Volume of the well = Volume of the rectangular field
Volume of the rectangular field = 385 m³ = 30 m × 20 m × height
$\mathrm{Height}=\frac{385{\mathrm{cm}}^2}{30\mathrm{m}\times 20\mathrm{m}}=0.641\mathrm{m}=64.1\mathrm{cm}$

Hence, the height through which the level of the field is raised is 64.1 cm.