Question

A cylindrical well of height 80 metres and radius 7 metres is dug in a field 28 metres long and 22 metres wide. The earth taken out is spread evenly on the field. What is the increase (in metres) in the level of the field?

Answer 1

Answer:

The increase in the level of the field is 26.6 m .

Step-by-step explanation:

Formula

Area of a rectangle =  Length × Breadth

$Area\ of\ circle = \pi r^{2}$

$Area\ of\ a\ cylinder = \pi r^{2} h$

Where r is the radius and h is the height .

As given

A cylindrical well of height 80 metres and radius 7 metres is dug in a field 28 metres long and 22 metres wide.

Thus

Area remains around cylinderical well = Area of rectangle - Area of circle.

Area remains around cylinderical well  = Area of the field - Area of the cylindrical well .

$\pi = 3.14$

Putting all the values in the above

Area remains around digging area = 28 × 22 - 3.14 × 7 × 7

                                                          = 616 - 153.86

                                                          = 462.14 m²

Thus

Now

Volume of dugged cylindrical well  = 3.14 × 7 × 7 × 80

                                                          = 12308.8 cm ³

Thus

As given

The earth taken out is spread evenly on the field.

Thus

Voulme of the  increase in the level of the field =  Volume of the dugged cylindrical well .

(As the field is in the form of cuboid having length , breadth and height. )

Length × Breadth × Height = 12308.8

Area remains around digging area × Height = 12308.8

Putting all the values in the above

462.14 × Height = 12308.8

$Height = \frac{12308.8}{462.14}$

Height = 26.6m (Approx)

Therefore the increase in the level of the field is 26.6 m .