Math unit 10

sphere

Definition of a Sphere. A sphere is a geometrical figure that is perfectly round, 3-dimensional and circular - like a ball. Geometrically, a sphere is defined as the set of all points equidistant from a single point in space.

Polyhedron

a solid figure with many plane faces, typically more than six.

Density

density = Mass/volume example: a clump of metal with mass 351.4 grams is dropped into a cylindrical container of water causing the water to rise 1.1 centimeters. the radius of base of container is 3 centimeters. what is the density of the metal.

right cone

noun, Geometry. 1. a cone whose surface is generated by lines joining a fixed point to the points of a circle, the fixed point lying on a perpendicular through the center of the circle. Compare oblique circular cone.

volume

the measure of the amount of space contained in a solid Area of base x height notation: use cubic units ³

sphere surface area conjecture

the surface area, s, of a sphere with radius r is given by the formula S = 4π r²

Prism-cylinder volume conjecture

the volume of a prism or cylinder is the area of the base multiplied by the height volume = Base area x Height of prism or Cylinder

Sphere volume conjecture

the volume of a sphere with radius r is given by the formula V = 4/3 π r³

Displacement

the volume of fluid that rises above the original fluid line when a solid object is submerged

oblique

this adjective refers to geometric lines or planes that are not parallel or perpendicular to a line or surface. A playground is positioned at an oblique angle to the ground.

cone

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.

great circle

A great circle, also known as an orthodrome, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere. ... The minor arc of a great circle between two points is the shortest surface-path between them.

lateral edges

A lateral edge is the intersection of two lateral faces. Sounds either germy or painful. The altitude of the prism is its height.

center

Center of a circle. The center of a circle is the point which is equidistant from all points on the circle. ... The center point is often used to label the whole circle. The figure below would be called "the circle C".

regular polyhedron

A polyhedron whose faces are identical regular polygons. Such as this Dodecahedron (notice that each face is an identical regular pentagon). There are five convex regular polyhedra, known as the Platonic Solids. And there are also four regular "star polyhedra", known as Kepler-Poinsot solids. See: Regular Polygon.

pyramid

A pyramid is a polyhedron that has a base, which can be any polygon, and three or more triangular faces that meet at a point called the apex. These triangular sides are sometimes called the lateral faces to distinguish them from the base.

prism

A solid object with two identical ends and flat sides. The shape of the ends give the prism a name, such as "triangular prism" • The cross section is the same all along its length. • The sides are parallelograms (4-sided shape with opposites sides parallel)

edge

An edge is a line segment that joins two vertices (on the boundary or where faces meet). Example: This tetrahedron has 6 edges. Vertices, Edges and Faces.

axis

Axis (plural - axes) - Definition and Meaning. A fixed reference line for the measurement of coordinates. In a two-dimensional coordinate system, a horizontal axis is often referred to as the x-axis and a vertical axis is referred to as the y-axis.

oblique cylinder

Definition: An oblique cylinder is one that 'leans over' - where the sides are not perpendicular to the bases. Opposite of a 'right cylinder'. Try this Drag the orange dot to reshape the cylinder. Note when it is a right cylinder and when it is oblique.

faces

Face. In any geometric solid that is composed of flat surfaces, each flat surface is called a face. The line where two faces meet is called an edge. For example, the cube above has six faces, each of which is a square.

vertex

From Latin: vertex "highest point" Definition: The common endpoint of two or more rays or line segments. Vertex typically means a corner or a point where lines meet. For example a square has four corners, each is called a vertex. The plural form of vertex is vertices.

right prism

Image result for right prism math definitionmath.tutorvista.com A right prism is a prism in which the joining edges and faces are perpendicular to the base faces. This applies if the joining faces are rectangular. If the joining edges and faces are not perpendicular to the base faces, it is called an oblique prism.

radius

In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the Latin radius, meaning ray but also the spoke of a chariot wheel.

hemisphere

In geometry it is an exact half of a sphere. It also refers to half of the Earth, such as the "Northern Hemisphere" (that part of the Earth north of the equator), or "Western Hemisphere" (the half of the Earth west of a line running from the North Pole through England to the South Pole, includes the Americas) Sphere.

tetahedron

In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces.

altitude

In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex). This line containing the opposite side is called the extended base of the altitude.

lateral

Lateral surface area is finding the area of the sides of a three-dimensional geometric figure. The formulas for lateral surface area are based on the base of the figure and whether the figure is a prism, cone, or pyramid.

bases

The surface a solid object stands on, or the bottom line of a shape such as a triangle or rectangle. But the top is also called a base when it is parallel to the bottom!

Pyramid-Cone Volume Conjecture

The volume of a cone or a pyramid is the area of the base multiplied by the height divided by three V= BH/3 = 1/3 BH where B is the area of the base, H is the height of the pyramid/ cone

height

Vertical distance from the top of an object or figure to its base is called Height.

cylinder

When the axis is perpendicular to the plane of the curve, the cylinder is called a right cylinder. In non-mathematical usage, both right and circular are usually implied. (geometry) A solid figure bounded by a cylinder and two parallel planes intersecting the cylinder. Any object in the form of a circular cylinder.

right cylinder

a cylinder with the bases circular and with the axis joining the two centers of the bases perpendicular to the planes of the two bases. See right circular cylinder defined for kids.