11.4 Solids, surface area

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oblique cone

A cone with an axis that is NOT the altitude

face

A flat surface of a polyhedron...a polygon in this case

Prism

A polyhedron with two congruent parallel bases.

polyhedron

A solid figure that is bounded by polygons that enclose a single region of space.

NOT polyhedral solid definition and examples

A solid that has curved surfaces Ex. Cylinder, cone, sphere

Euler's (Oiler's) Theorem

In a polyhedron... number of faces plus the number of vertices equals the number of edges plus two F + V = E + 2

Base

Polygon that is used to name the polyhedron

Two types of solids are

Polyhedral (all sides made of polygons) and NOT polyhedral (has curved surfaces)

Surface Area of a Right Cylinder

S=2B+Ch or (2πr²+2πrh) where B is the AREA of the base, C is the circumference, and h is the height of the cylinder

Surface Area of a Right Prism

S=2B+Ph where B is the AREA of the base, P is perimeter, and h is the height of the prism

Surface Area of a Pyramid

SA = B + 1/2Pl where "P" is the perimeter and "l" is the slant height

Surface Area of a Cone

SA = πr² + πrl

surface area

SUM of the AREAS of ALL FACES

cross section

The intersection of a plane and a solid.

right cone

a cone with an axis that is also an altitude

oblique cylinder

a cylinder whose axis is not perpendicular to the bases

right cylinder

a cylinder whose axis is perpendicular to its bases

vertex

a point where 3 or more EDGES meet

regular polyhedron

a polyhedron in which all of the faces are REGULAR CONGRUENT polygons

oblique prism

a prism with lateral edges that are not perpendicular to the bases

regular pyramid

a pyramid whose base is a regular polygon, altitude has an endpoint at the center of the base, and whose lateral faces are congruent isosceles triangles

egde

a segment formed by the intersection of two FACES

polyhedral solid definition and examples

a solid figure made of faces that are polygons Ex. Prisms and pyramids

convex polyhedron

any two points on its surface can be connected by a segment that lies entirely INSIDE or ON the polyhedron

right prism

each lateral edge is perpendicular to both bases

Concave polyhedron

if any two points on its surface can be connected by a segment that lies partially OUTSIDE the polyhedron

The lateral faces of a prism are

parallelograms

Lateral edges of a prism are

segments connecting corresponding vertices of the bases of a prism

slant height of a pyramid or cone

the height of a lateral face of a pyramid or cone

lateral area

the sum of the areas of the lateral faces

Net of a polyhedron

two-dimensional representation of the faces of a polyhedron (like an unfolded box)


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