PPMS Geometry 3D
Terms
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- Solid
- Is a 3 dimensional object.
- Faces
- A flat surface on a solid.
- Polyhedrons
- A solid whose faces are polygons.
- Edges
- A segment joining two faces of a polyhedron.
- Vertices
- Corners of a solid.
- Prism
-
A polyhedron whose bases are congruent and parallel.
Example:
rectangular prism (flat side lunch box - pyramid
-
A polyhedron with one polygonal base.
Example: The egyptian pyramids have a
square base. (Square Pyramid) -
Describe a pentagonal pyramid.
Number of faces:
Number of edges:
Number of vertices: -
Number of faces: 6
Number of edges: 10
Number of vertices: 6 -
Describe a pentagonal prism.
Number of faces:
Number of edges:
Number of vertices: -
Number of faces: 7
Number of edges: 15
Number of vertices: 10 - surface area (for a solid)
- The sum of the areas of its surfaces.
- What is the best way to find the surface area of a solid?
-
Drawing a net.
Allows you to see all the shapes and dimensions of its faces. Then you just use the area formulas to help you calculate the sufrace area. - Volume (three dimensional object)
- The amount of space the object takes up.
- Volume is always measured in?
-
Cubic units
Just need to count up number of cubes an object can hold. - What is the volume of a rectangular prism with a lenght of 10 in, a width of 5 in, and a height of 10 in?
-
Answer: 500 cubic inches
or 500 in³ - Circle
- A plane figure whose points are all the same distance from its center.
- Center
- The point in the exact middle of a circle or sphere.
- central angle
- An angle whose vertex is at the center of a circle.
- Pi
- The ratio of a circle's circumference to its diameter. Value = 3.14159265...
- diameter
- The distance across a circle through its center.
- radius
- The distance from the center of the circle to a point on the circle.
- Circumference
-
The perimeter of a circle.
Ex. The distance around your pool. - Formula for Circumference
- C = 3.14159265 x diameter
- Find the circumference of a circle whose radius is 5 cm.(Use 3.14)
- Answer: 3.14 x 10 = 31.4 cm
- What is the formula for area of a circle?
-
Area = pi x radius squared
= 3.14 x r² - Find the area of a circle with a radius of 10 cm.
-
Area = 3.14 x 10²
Area = 314 cm2 - All faces of polyhedrons are flat. True or False
- True
- cylinder
- A solid with two parallel circular bases with the same radius.
- cone
- A solid with one circular base.
- sphere
-
Is a solid version of a circle. (ball)
All the points on a sphere ae the same distance from its center. - The net of of cylinder always has what 3 figures to measure?
- 2 circles and 1 rectangle
- What is the formula for the volume of a cylinder?
-
V = Bh
B = pi x radius squared
h = height
3.14 x r² x height = ____ units³ -
What is the volume of a cylinder with a radius of 3ft and the height 5ft?
(Round to the nearest tenth) -
Answer: 141.3 ft
V = 3.14 x 3² x 5³