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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.