Mensuration Lectures
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Transcript of Mensuration Lectures
1/15/2014
1
SolidSolid
MENSURATIONMENSURATION
ROY D. TIPONES, PECE
Solid Solid -- polyhedronspolyhedrons
• Is a solid whose faces are plane polygons. A
regular polyhedron is a solid with all its faces
identical regular polygons. There are only five
regular polyhedrons, namely tetrahedron,
hexahedron (cube), octahedron,
dodecahedron and icosahedron. These solids
are also known as Platonic solids in honor of
Plato (427-348 BC)
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Common polyhedronsCommon polyhedrons
• Cube is a polyhedron with all six faces a
square.
• Rectangular parallelepiped is a
polyhedron with all six faces a rectangle.
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PrismsPrisms
• Is a polyhedron with two faces (bases) parallel
and congruent and whose remaining faces
(lateral faces) are parallelograms.
• Right prism is one which has its lateral faces
perpendicular to the base.
PrismsPrisms
• Oblique prism is one which has its lateral
faces not perpendicular to the base.
• Truncated prism is a portion of a prism
contained between the base and a plane that
is not parallel to the base.
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CylinderCylinder
� Is a solid bounded by a closed cylindrical surface and
two parallel planes.
Pyramids and ConesPyramids and Cones
• Pyramid is a polyhedron of which one face, called the base, is a polygon of
any number of sides and the other faces are triangles which have a
common vertex.
• Cone is a solid bounded by a conical surface (lateral surface) whose
directrix is a closed curve, and a plane (base) which cuts all the elements.
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FrustumFrustum
• Frustum (of a pyramid/cone) is a portion of
the pyramid/cone included between the base
and a section parallel to the base.
PrismatoidPrismatoid
• Is a polyhedron having for bases two polygons
in parallel and for lateral faces triangles or
trapezoids with one side lying in one base, and
the opposite vertex or side lying in the other
base of the polyhedron.
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SphereSphere
• Is a solid bounded by a closed surface every
point of which is equidistant from a point
called center.
SphereSphere
• Zone is the portion of the surface of a sphere
included between two parallel planes.
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SphereSphere
• Spherical Segment – is a solid bounded by a
zone and the planes of the zone’s base.
SphereSphere
• Spherical Sector – is a solid generated by
rotating a sector of a circle about an axis
which passes through the center of the circle
but which contains no point inside the sector.
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SphereSphere
• Spherical Pyramid – is a pyramid formed by a
portion of a surface of a sphere as base and
whose elements are the edges from the
vertices of the base to the center of the
sphere.
SphereSphere
• Spherical Wedge – is a portion of a sphere
bounded by two half great circles and an
included arc.
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TorusTorus
• Torus – is a solid formed by revolving a circle
about a line not intersecting it.
EllipsoidEllipsoid
• Ellipsoid (Spheroid) – is a solid formed by
revolving an ellipse about its axis.
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EllipsoidEllipsoid
• Prolate Spheroid – is a solid formed by
revolving an ellipse about its major axis.
• Oblate Spheroid – is a solid formed by
revolving an ellipse about its minor axis.