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
Solution:-
Given:-
- Diameter of the well = 7 m
- Radius of the well = 7/2 m
- Depth of the well = 20 m
According to the Given Information:-
Shape of well is in the form of Cylinder and shape of platform is in the form of Cuboid.
=) Volume of the mud dug from the well = Volume of Cylinder
=) Volume of Cylinder = πr²h
=) Volume of Cylinder = (22/7) × (7/2) × (7/2) × 20
=) Volume of Cylinder = 770 m³
Now,
The duged out mud is used to made the platform which is in the form of Cuboid.
=) Volume of Cuboid = Volume of Cylinder
=) 22 x 14 x h = 770
=) h = 770 / 22x14
=) h = 2.5 m
Hence,
Height of the platform is of 2.5m
Figure:-
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.
