
Solid
Geometry 


Solids
of Revolution 
Cylinder

Cone

Conical
frustum

Sphere

Spherical
cap 
Spherical
segment 
Spherical
sector 





Solid
of revolution 
A
solid figure generated by revolving a line or curve (the
generator) around a fixed axis. 

Cylinder 
A cylinder is solid of revolution
generated by rotation of rectangular around one of its sides as the axis of
revolution. 


S
= 2B + S_{lat}
= 2· r^{2}p^{ }_{
}+ 2rp
· h
= 2rp·(r
+ h) 

surface 
V
= B · h = r^{2}p
· h 

volume 



Cone

A cone is solid of revolution generated
by rotation of a right triangle around one of its legs as the axis of revolution. 

S
= B + S_{lat}
= r^{2}p^{ }_{
}+ rp
s = rp
(r + s) 

surface 

V
= 1/3 ·
B · h = 1/3
r^{2}p
· h 

volume 


Conical
frustum 



Sphere

A sphere is generated by rotation of
a semicircle around its diameter. 



S
= 4p r^{2} 

surface 
V
= 4/3p r^{3}


volume 


Spherical cap 





surface 


volume 


volume 


Spherical
segment 



Spherical
sector 



surface 


volume 









Geometry
and use of trigonometry contents  B 



Copyright
© 2004  2020, Nabla Ltd. All rights reserved. 