A 20m deep well with diameter 7m is dug and the earth from digging is evenly spread out to form a platform 22m by 14m . The approx height (in m) of platform is ?
Answers
Height of the well = 20m
Diameter of the well = 7 m
So Radius of the well = 7/2 = 3.5cm
Volume of the well = Volume of the cylinder
= πr²h
= 22/7 × 3.5 × 3.5 × 20
= 770 m³
Since the mud that is dug out from well is spread over the ground to form a platform
Length of the platform = 22m
Breadth of the platform = 14m
Let the height of the platform be h m
So Volume of the platform = Volume of the well
Length × Breadth × Height = 770 m³
22 m × 14m × h = 770
308 × h = 770
h = 770/308
h= 2.5 m
So, Height of the platform = 2.5m
Given:-
- Depth (h) of well = 20m.
- Radius (r) of circular end of well = 7/2 m.
To find:-
- Find the height of platform is ?
Solutions:-
- Let height of the platform = h
Area of platform = length × breadth
=> 22 × 14
=> 308m²
Volume of soil dug from the well will be equal to the volume of soil scattered on the platform.
Volume of soil from well = Volume of soil used to makes sure platform.
=> πr²h = Area of platform × height of platform
=> π × (7/2)² × 308 × h
=> π × 49/4 × 20 = 308 × h
=>h = 22/7 × 49/4 × 20/308
=> h = 11 × 7/2 × 10/154
=> h = 77/2 × 10/154
=> h = 10/4
=> h = 5/2
=> h = 2.5m
Hence, the height of platform is 2.5m.
Some Important:-
- Volume of cylinder ( Area of base × height ). = (πr²) × h
= πr²h
- Curved surface = ( Perimeter of base ) × height.
= (2πr) × h
= 2πrh
- Total surface are = Area of circular ends + curved surface area.
= 2πr² + 2πrh
= 2πr(r + h)
Where,
r = radius of the circular base of the cylinder.
h = height of cylinder.