Question

In the middle of a rectangular field measuring 30 m ×20 m, 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

Given,

Diameter of well = 7 m

Radius of well = \(\frac{7}{2}\) = 3.5 m

Depth of well = 10 m

Volume of well = πr²h = \(\frac{22}{7}\) x 3.5 x 3.5 x 10 m³

volume of well = Area of spread out × height of embankment

= \(\frac{22}{7}\) x 3.5 x 3.5 x 10 = 30 x 20 - \(\frac{22}{7}\) x \(\frac{7}{2}\)  x \(\frac{7}{2}\) x h

= \(\frac{22}{7}\) x 3.5 x 3.5 x 10 = \(\frac{1123}{2}\) x h

= h = \(\frac{22\times 35}{1123}\) = 68.56 cm

Height of embankment = 68.6 cm