Find the volume of a solid in the form of a right circular cylinder with hemi-spherical ends whose total length is 2.7 m and the diameter of each hemi-spherical end is 0.7 m.
Answers
Answer:
The Volume of solid is 0.95 m³
Step-by-step explanation:
SOLUTION :
Given :
Diameter of cylinder and hemispherical ends = 0.7 m
Radius of cylinder and hemispherical ends = 0.7/2 = 7/20 m
Total length of a solid = 2.7 m
Height of a cylinder, h = Total length of a solid - 2 × Radius of hemisphere
Height of a cylinder, h = 2.7 - 2 × 7/20
h = 2.7 - 7/10 = 2.7 - 0.7 = 2 m
h = 2 m
Volume of solid,V = Volume of Cylinder + Volume of two hemispheres
V = πr²h + 2 × 2/3πr³
V = πr²h + 4/3πr³
V = πr²(h + 4/3r)
V = 22/7 × (7/20)² (2 + 4/3 × 7/20)
V = 22/7 × 49/400 (2 + 7/15)
V = (11 × 7)/200 × 37/15
V = 77/200 × 37/15
V = 2849/3000
V = 0.95 m³
Hence, the Volume of solid is 0.95 m³
HOPE THIS ANSWER WILL HELP YOU…
Answer:
Volume of solid=πr
2
h+2×
3
2
πr
3
⇒πr
2
[h+
3
4
r]=
7
22
×(
2
0.7
)
2
[(2.7−2×
2
0.7
)+
3
4
×
2
0.7
]
=
7
22
×
2
0.7
×
2
0.7
×2.47=0.95m
3