Volume & surface area of solid
figures
Calculus
University of Asia and the Pacific
1 pag.
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Volume & surface area of solid figures – sphere, cube, rectangular solid (box) with and without
top, cylinder, and cone.
Figure
Sphere
Volume
4
V = πr3 ,
3
r radius
Surface Area
S = 4π r 2 ,
r radius
Cube
V = s 3 , s side
S = 6s 2 , s side
Rectangular Solid
V = A2 h , A2 is area of the
base, h height.
S = 2lw + 2lh + 2wh
V = lwh , l length, w width, h
height.
= 2(lw + lh + wh )
l length, w width, h height.
V = π r 2 h , r radius, h height
S=
Prisms: Parallel flat
polygon top and bottom
(bases).
V = A2 h , A2 is area of the
base, h height.
Calculus topic – to come
Pyrimids (polygon base to a
point)
1
Ah , A is area of the
3
base, h height.
Calculus topic – to come
1 2
π r h , r is the radius of
3
the circular base, h height
Stotal =
Cylinder
V =
V =
2
2π r 2
top & bottom
r +h
+ 2π rh
lateral side
π r 2 + π r r 2 + h2 ,
base area
2
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lateral area
is slant height