11.4 Solids, surface area
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)