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Platonic Solids
A polyhedron is a three-dimensional object with flat faces, and straight edges. cubes, prisms, and pyramids are examples of a polyhedra.
there are common polyhedra.
platonic solids: is a three-dimensional shape. the five platonic solids are, tetrahedron, cube, octahedron, icosahedron, dodecahedron.
there are common polyhedra.
platonic solids: is a three-dimensional shape. the five platonic solids are, tetrahedron, cube, octahedron, icosahedron, dodecahedron.
Cube: 6 faces, 12 edges, 8 vertices
Tetrahedron: 4 faces, 6 edges, 4 vertices
Octahedron: 8 faces, 12 edges, 6 vertices
Dodecagon: 12 faces, 30 edges, 20 vertices
Icosahedron: 20 faces, 30 edges, 12 vertices
Tetrahedron: 4 faces, 6 edges, 4 vertices
Octahedron: 8 faces, 12 edges, 6 vertices
Dodecagon: 12 faces, 30 edges, 20 vertices
Icosahedron: 20 faces, 30 edges, 12 vertices
how to get the area of a three-dimensional figure
the surface area of a three-dimensional figure is the sum of the areas of all of its surfaces. the lateral area of a three-dimensional figure is the surface area excluding the area of any bases . area is measured in square units.
- how to find the lateral area and surface area of a right prism and a right cylinder.
The lateral area is the surface area of a 3D figure, but excluding the area of any bases. Lateral Area is often abbreviated L.A.
Right Prism The lateral area L (area of the vertical sides only) of any right prism is equal to the perimeter of the base times the height of the prism (L = Ph).
The total area T of any right prism is equal to two times the area of the base plus the lateral area.
Formula: T = 2B + Ph
Right cylinder
Lateral Area of a cylinder: circumference × height.
Right Prism The lateral area L (area of the vertical sides only) of any right prism is equal to the perimeter of the base times the height of the prism (L = Ph).
The total area T of any right prism is equal to two times the area of the base plus the lateral area.
Formula: T = 2B + Ph
Right cylinder
Lateral Area of a cylinder: circumference × height.
formulas to find the lateral area
Lateral Area of a prism: perimeter × height
Lateral Area of a cylinder: circumference × height.
Lateral Area of a regular pyramid: ½ perimeter × slant height.
Lateral Area of a right cone: ½ perimeter × slant height.
Lateral Area of a cylinder: circumference × height.
Lateral Area of a regular pyramid: ½ perimeter × slant height.
Lateral Area of a right cone: ½ perimeter × slant height.
how to find the volume of...
right cylinder
Although a cylinder is technically not a prism, it shares many of the properties of a prism. Like prisms, the volume is found by multiplying the area of one end of the cylinder (base) by its height.
Since the end (base) of a cylinder is a circle, the area of that circle is given byMultiplying by the height h we get where:
π is Pi, approximately 3.142
r is the radius of the circular end of the cylinder
h height of the cylinder
Right Prism
The volume V of any right prism is the product of B, the area of the base, and the height h of the prism. The volume V of any right prism is the product of B, the area of the base, and the height h of the prism.
Formula: V = Bh
circular Cone Volume
The volume V of any cone with radius r and height h is equal to one-third the product of the height and the area of the base.
Formula: V = (1/3)(PI)r2h
Pyramid
The volume V of any pyramid with height h and a base with area B is equal to one-third the product of the height and the area of the base.
Formula: V = (1/3)Bh
Although a cylinder is technically not a prism, it shares many of the properties of a prism. Like prisms, the volume is found by multiplying the area of one end of the cylinder (base) by its height.
Since the end (base) of a cylinder is a circle, the area of that circle is given byMultiplying by the height h we get where:
π is Pi, approximately 3.142
r is the radius of the circular end of the cylinder
h height of the cylinder
Right Prism
The volume V of any right prism is the product of B, the area of the base, and the height h of the prism. The volume V of any right prism is the product of B, the area of the base, and the height h of the prism.
Formula: V = Bh
circular Cone Volume
The volume V of any cone with radius r and height h is equal to one-third the product of the height and the area of the base.
Formula: V = (1/3)(PI)r2h
Pyramid
The volume V of any pyramid with height h and a base with area B is equal to one-third the product of the height and the area of the base.
Formula: V = (1/3)Bh
congruent or similar solids
Two solids are similar if they have the same shape and the ratios of their corresponding linear measures are equal.
two solids are congruent if they have the following characteristics:
two solids are congruent if they have the following characteristics:
- corresponding angles are congruent
- corresponding edges are congruent
- corresponding faces are congruent
- volumes are equal
Learning Goals
- The student will find the surface area of three-dimensional solids.
- The student will find the lateral area and surface area of a right prism and a
- right cylinder.
- The student will find the lateral area and surface area of a regular pyramid
- and a right circular cone.
- The student will find the volume of a right prism and a right cylinder.
- The student will find the volume of a pyramid and circular cone.
- The student will identify congruent or similar solids and state the properties of congruent solids.