A boiler is in the form of a cylinder 2 m long with hemispherical ends each of 2 metre diameter. Find the volume of the boiler.
Answers
Answer:
The volume of the boiler is 220/21 m³
Step-by-step explanation:
SOLUTION :
Given :
Diameter of the hemisphere = 2 m
Radius of the Cylinder & hemisphere, r = 1 m
Height of the cylinder , h = 2 m
Total volume of the boiler = Volume of the cylindrical portion + Volume of the two hemispheres
V = πr²h + 2(2/3 πr³)
V = πr²h + 4/3 πr³
V = πr²(h + 4/3 r)
V = 22/7 × 1² ( 2 + 4/3 ×1)
V = 22/7 × 1× (2 + 4/3)
V = 22/7[(6+4)/3]
V = 22/7 × 10/3 = 220/21
V = 220/21 m³
Hence,the volume of the boiler is 220/21 m³
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answer :-
given :-
according to the question, A boiler is in the form of a cylinder 2 m long with hemispherical ends each of 2 metre diameter.
height (long) of the cylindrical part = 2m
diameter of the hemispherical part = 2m
therefore it's radius = 2/2 (since we know that the Length of radius is half of it's diameter)
= 1m
volume of both the hemispherical part = 2 (2/3πr³) (since we are finding the volume of both the hemispherical parts)
= 2 × 2/3 × 22/7 × 1 × 1 × 1
= 88/21cm³
volume of the cylindrical part = πr²h
= 22/7 × 1 × 1 × 2
= 44/7cm³
therefore total volume of the boiler = 88/21 + 44/7
= 88/21 + 132/21
= 220/7cm³ or 31.43cm³ (approximately)