Question

7. How many cubic metres of earth must be dug out to sink a well which is 20 m deep and
a diameter of 7 metres? If the earth so dug out is spread over a rectangular plot 28m by
11 m, what is the height of the platform so formed?​

Answer 1

Answer:

i) The amount of Earth dug = Volume of the well

As the well is cylindrical in shape,

Volume(well) = Volume(Cylinder)

Cylinder: h = 20m, d = 7m => r = 3.5m

Volume = πr²h

= (22/7)(3.5)²(20)

= 22(0.5)(3.5)(20)

= 11(70)

= 770m³

Therefore, 770m³ of earth must be dug out.

ii) Volume of Platform = Volume of Earth dug out.

As platform is cuboidal in shape,

Volume of platform = Volume of cuboid.

Cuboid: l = 28m, b = 11m

=> lbh = 770

=> h = 770/(lb)

=> h = 770/(11*28)

=> h = 70/28

=> h = 5/2

Therefore, the height of the platform is 2.5m