A well 20m deep with diameter 7m is spread out on a rectangular plot 22m long and 14m broad ------?

Question

Please find the height of the platform so formed ?

Please solve this in steps as I want this for my holiday homework.

Answer 1

Assuming the walls of the well are neglibly thick:

A1 = 2pi*r ( r + h) = 2*pi*3.5*(3.5+h) = 24.5pi + 7pi*h

A2 = 22*14 = 308

A1=A2

Rearranging gives:

h = (308 - 24.5pi)/(7pi) = 10.5m

Answer 2

First work out the volume of the well, then what height gives you the same volume on the rectangular plot.

Volume = 2pi X r^2 x h = 2pi x 3.5^2 x 20 m^3

When you spread this on a plot with area 22 x 14 m = 308 m^2, the height will be the volume of the well divided by this area.

So height = 2pi x 3.5^2 x 20 / 308 = 4.998 m.

Answer 3

The volume of well = pi*r*r*h
The volume of the platform = L*B*H

Volume of well = volume of platform.

i.e. pi*r*r*h = L*B*H

pi = 22/7
r = D/2 = 7/2
h = 20

L = 22
B = 14
H =?

puting in equation

22/7*7/2*7/2*20 = 22*14* H

transposing and calculating

=> (11*7*20) / (2*22*14) = H
=> 10/4 = H
=> H = 2.5 m

Therefore the height of the platform is 2.5 meters.

Answer 4

Volume of water = π x 3.5² x 20 m³
Volume of water = 769.7 m³
769.7 = 22 x 14 x h
h = 769.7 / (22 x 14) m
h = 2.5 m
Height of platform = 2.5 m