Solid
figures
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Pyramid
|
A
solid whose base is a polygon and whose lateral faces are
triangles with a common vertex (apex) is called a pyramid. |
A
right pyramid is a pyramid in which the line joining
the centroid of the base (the point of coincidence of the medians) and the apex is perpendicular to the base. |
A
regular pyramid is a right pyramid whose base is a regular polygon and
lateral faces are congruent isosceles triangles. |
The volume of a pyramid is one third of the product of the area of the base and the perpendicular distance from the vertex to the base. |
The surface
area of a pyramid, S
= B
+ Slat |
The volume of a
pyramid,
V
= (1/3) ·
B ·
h
|
where,
B is
the base area, Slat
is the lateral surface area and h
is the height of the
pyramid. |
|
Regular
square pyramid
|
A
regular square pyramid has square base and lateral faces are
four congruent isosceles triangles making the same angle with
the base.
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Regular triangular pyramid
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Regular hexagonal pyramid
|
A
regular hexagonal pyramid has a regular hexagon base, and six congruent isosceles triangles as lateral faces making the same angle with
the base.
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Right
pyramidal frustum
|
|
B
: B1 = (h + x)2
: x2,
where |
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|
-
surface |
|
P,
P1 - bottom
and top base perimeter |
|
-
volume |
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Regular Polyhedrons
|
Tetrahedron,
octahedron, icosahedron
and dodecahedron
|
The equilateral triangles are faces of, the tetrahedron (4-faced), the
octahedron (8) and the icosahedron (20), while the
dodecahedron
consists of 12 regular pentagons. |
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Solids
of revolution
|
A
solid figure generated by revolving a line, curve or a plane
figure around a fixed axis is called a solid of
revolution.
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Cylinder
|
A cylinder is solid of revolution
generated by rotation of rectangular around one of its sides as the axis of
revolution. |
|
S
= 2B + Slat
= 2· r2p
+ 2rp
· h
= 2rp·(r
+ h) -
surface
|
V
= B · h = r2p
· h - volume
|
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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 + Slat
= r2p
+ rp
s = rp
(r + s) -
surface, |
V
= (1/3) ·
B · h = 1/3
r2p
· h - volume |
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Conical
frustum
|
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Sphere
|
A sphere is generated by rotation of
a semicircle around its diameter. |
|
|
S
= 4p r2
-
surface |
V
= (4/3)p r3
-
volume |
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Spherical cap
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-
surface |
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-
volume |
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-
volume |
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Spherical
segment
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Spherical
sector
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