Geometry Test Chapter 11
central angle of a regular polygon
A central angle of a regular polygon is an angle formed by two radii drawn to consecutive vertices of the polygon. To find the measure of each central angle, divide 360 degrees by the number of sides.
chord of a sphere
A chord of a sphere is a segment whose endpoints are on the sphere
diameter of a sphere
A diameter of a sphere is a chord that contains the center.
Convex
A polyhedron is convex if any two points on its surface can be connected by a segment that lies entirely inside or on the polyhedron
regular polyhedron
A polyhedron is regular if all of its faces are congruent regular polygons
radius of a sphere
A radius of a sphere is a segment from the center to a point on the sphere
Sector
A sector of a circle is the region bounded by two radii of the circle and their intercepted arc
sphere and center of the sphere
A sphere is the set of all points in space equidistant from a given point. This point is called the center of the sphere.
hemispheres
Every great circle of a sphere separates the sphere into two congruent halves called hemispheres.
great circle
If a plane intersects a sphere, the intersection is either a single point or a circle. If the plane contains the center of the sphere, then the intersection is a great circle of the sphere. The circumference of a great circle is the circumference of the sphere.
Concave
If this segment goes outside the polyhedron, then the polyhedron is nonconvex, or concave
Postulate 28 Volume Congruence Postulate
If two polyhedra are congruent, then they have the same volume.
Theorem 11.13 Similar Solids Theorem
If two similar solids have a scale factor of a:b, then corresponding areas have a ratio of a²:b², and corresponding volumes have a ratio of a³:b³
Arc Length Corollary
In a circle, the ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to 360 degrees
Theorem 11.2 Area of a Circle
The area of a circle is pi times the square of the radius.
Theorem 11.4 Area of a Regular Polygon
The area of a regular n-gon with side length s is one half the product of the apothem a and the perimeter p. A=1/2aP or 1/2a x ns
The center of the polygon and the radius of the polygon
The center of the polygon and the radius of the polygon are the center and the radius of its circumscribed circle.
Theorem 11.1 Circumference of a Circle
The circumference C of a circle is C = πd or C = 2πr, where d is the diameter of the circle and r is the radius of the circle.
apothem of the polygon
The distance from the center to any side of the polygon is called the apothem of the polygon. The apothem is the height to the base of an isosceles triangle that has two radii as legs.
Theoren 11.5 Euler's Theorem
The number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula F + V = E + 2.
Theorem 11.3 Area of a Sector
The ratio of the area of a sector of a circle to the area of the whole circle (πr²) is equal to the ratio of the measure of the intercepted arc to 360 degrees
Theorem 11.11 Surface Area of a Sphere
The surface area S of a sphere is S=4πr², where r is the radius of the sphere.
Theorem 11.10 Volume of a Cone
The volume V of a cone is V = 1/3Bh=1/3 πr²h, where B is the area of the base, h is the height, and r is the radius of the base.
Theorem 11.7 Volume of a Cylinder
The volume V of a cylinder is V = Bh = πr²h, where B is the area of a base, h is the height, and r is the radius of a base.
Theorem 11.6 Volume of a Prism
The volume V of a prism is V = Bh, where B is the area of a base and h is the height
Theorem 11.9 Volume of a Pyramid
The volume V of a pyramid is V = 1/3 Bh, where B is the area of the base and h is the height.
Theorem 11.12 Volume of a Sphere
The volume V of a sphere is V=4/3πr³, where r is the radius of the sphere.
Postulate 27 Volume of a Cube Postulate
The volume of a cube is the cube of the length of its side
volume
The volume of a solid is the number of cubic units contained in its interior. Volume is measured in cubic units, such as cubic centimeters (cm³)
Postulate 29 Volume Addition Postulate
The volume of a solid is the sum of the volumes of all its nonoverlapping parts.
similar solids
Two solids of the same type with equal ratios of corresponding linear measures, such as heights or radii, are called similar solids
vertex of a polyhedron
a point where three or more edges meet. The plural of polyhedron is polyhedra or polyhedrons.
edge of a polyhedron
edge of a polyhedron is a line segment formed by the intersection of two faces
polyhedron and faces
s a solid that is bounded by polygons, called faces, that enclose a single region of space
cross sections
sections that are produced by a plane running through the solid