2- & 3-Dimensional Objects Flashcards
A regular polyhedron(all the sides are congruent & all the angles are congruent). There are only 5 regular polyhedral (tetrahedron, cube, octahedron, dodecahedron, or icosahedrons)
Platonic solid
an object composed of 3 or more closed sides
Polygon
On object made up of simple shapes, such as triangles, rectangles, trapezoids, &circles
Composite figure
A 3-dimensional figure whose surfaces are polygons
Polyhedron
The surfaces of a polyhedron
Face
a segment that is formed by the intersection of two faces
Edge
A point where three or more edges intersect
Vertex
A two-dimensional pattern that you can fold to form a three-dimensional figure
Net
A polyhedron with six faces, each of which is square
Cube
The space that a figure occupies. If is measured in cubic units
Volume
If two space figures have the same height and the same cross-sectional area at entry level, then they have the same volume
Cavalieri’s principle
The same shape and all their corresponding dimension are proportional
Similar solids
The ratio of corresponding linear dimensions of two similar solids
Similarity ratio
Intersection of a 3-dimensional figure and a plane
Cross-section
A polyhedron with exactly two congruent, parallel faces
Prism
The congruent and parallel faces of a prism
Bases
The non-parallel faces of a prism
Lateral faces
The perpendicular segment that hound the planes of the bases, aka height
Altitude of prism
The lateral faces are rectangles and the height is and edge of the prism
Right prisms
The lateral faces are rectangles and the height is outside the prism
Oblique prism
The sum of the areas of the lateral faces
Lateral area of prism
Sum of the lateral area and the area of the two bases
Surface area of a prism
The product of the area of a base and the height of the prism
Volume of a prism
Like a prism, has two congruent and parallel bases which are circles
Cylinder
A perpendicular segment that joins the planes of the bases
Altitude of a cylinder
The length of the altitude
Height of a cylinder
A cylinder whose height is located in the cylinder
Right cylinder
A cylinder whose height is located outside of the cylinder
Oblique cylinder
Area of the resulting rectangle when you “unroll” it
Lateral area of the cylinder
The sum of the lateral area and the areas of the two circular bases
Surface area of a cylinder
The product of the area of the base and the height of the cylinder
Volume of a cylinder
A polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces) are triangles that meet at a common vertex
Pyramid
Pyramids are named by?
The shape of its base
The perpendicular segment from the vertex to the planes of the base
Altitude of pyramid
The length of the altitude
Height of pyramid
A pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles
Regular pyramid
The length of the altitude of a lateral face of a pyramid
Slant height
The sum of the areas of the congruent lateral faces
Lateral area of pyramid
The sum of the areas of the congruent lateral faces and the area of the base
Surface area of a pyramid
1/3 the product of the area of the base and the height of the pyramid
Volume of a pyramid
A “pointed” like pyramid but it’s base is a circle
Cone
The altitude is a perpendicular segment from the vertex to the center of the base
Right cone
The length of the altitude
Height of cone
The distance from the vertex to a point on the edge of the base
Slant height of a cone
1/2 the perimeter of the base times the slant height
Lateral area of a cone
The sum of the lateral area and the area of the base
Surface area of a cone
1/3 the product of the area of the base and the height of the cone
Volume of cone
The set of all points in space equidistant from a given point called the center
Sphere
A segment that has one endpoint at the center and the other endpoint on the sphere
Radius
A segment passing through the center with end points on the sphere
Diameter
The center of the sphere is also the center of the center circle
Great circle
Circumference of the great circle is also that of the sphere
Circumference
What the great circle divides the sphere into
Hemispheres
Four times the product of pi and the square of the radius of the sphere
Surface area of a sphere
4/3 the product of pi and the cube of the radius of the sphere
Volume of a sphere
A line from the center of a regular polygon at right angles to any of its sides
Apothem
