Question

a 20m deep well with diameter 7m is dug and the earth is digging is evenly to form a platform 22m × 14m . Determine the height of the platform

Answer 1

diameter of well =7m
$radius = \frac{7}{2} m$
height of well = 20m

volume of earth dug=volume of earth present in cylinder

$volume = \pi {r}^{2} h$
$= \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 20 \\ = 770 {m}^{3}$
Now,

the volume of the Earth will be the same.

it is spread on a platform which will be obviously a rectangle . you can make it out from the variation between the measurements. But when the Earth is dug out from the well and spread over that area , there will be a rise in the height.

let height be 'h'

volume=length×breadth×height
770=22×14×h
$\frac{770}{22 \times 14} = h$
$h = \frac{5}{2} = 2.5m$

the rise is level or the height is 2.5 m

Answer 2

⇒ Given:- Height (h) of well :- 20m

Diameter (d) :- 7 m

Radius (r) :- 7/2 m

Volume of earth platform :- 22 m by 14m

⇒ To find :- Height of the platform:- ?

⇒ Solution:-

Volume of cylinder of radius 7/2 m and height 20 m

Volume of cylinder :- π(r^2)(h)

= 22/7×(7/2^2)×20 m^3

= 770 m^3

Let the height raised by 22 m × 14 m platform be equal to h metres

Therefore,

Volume of the earth in platform = Volume of the earth taken out of the well

22 × 14 × h = 770

h = 770/22 × 14 m

h = 5/2 m

h = 2.5 m

Hence , the height of the platform is 2.5 m.