Chapter 9 Flashcards
solids or solid figures
three dimensional shapes
polyhedron
a solid formed by polygons
faces
the plane surfaces
edges
the segments joining the vertices
Types of solids
Rectangular Prism, Triangular Prism, Cube (Square prism)
Rectangular pyramid, triangular pyramid, pentagonal pyramid
Cylinder, Cone, Sphere
Prism
a polyhedron with two congruent faces that lie in parallel planes
surface area
the sum of the areas of polyhedron’s faces
Lateral faces
faces of the prism that are not bases
Lateral area
the sum of the areas of the lateral faces
Surface area of a prism
Surface area = 2(area of base) + (perimeter of base)(height)
cylinder
a solid with two congruent circular bases that lie in parallel planes
The lateral area of a cylinder is the area of the curved surface
Surface area of a cylinder
Surface area = 2(area of bases) + (circumference of base)(height)
pyramid
a polygon and the lateral faces are triangles with a common vertex
height of a pyramid
the perpendicular distance between the vertex and base
slant height of a pyramid
the height of any of its lateral faces
(slant height)^2 = (height)^2 + (1/2 side)^2
Surface area of a pyramid
Surface area = (area of base) + 1/2(perimeter of base)(slant height)
cone
the solid has a circular base and a vertex that is not in the same plane as the base
height of a cone
the perpendicular distance between the vertex and the base
slant height of a cone
the distance between the vertex and a point on the base edge
Surface area of a cone
Surface area = (area of base) + (area of sector)
= (area of base) + 3.14(radius of base)(slant height)
volume
of cubit units contained in its interior
volume of a prism
Volume = (area of base)(height)
volume of a cylinder
Volume = (area of base)(height)
= 3.14(radius)^2 of height
Volume of a pyramid
Volume = 1/3(area of base)(height)
Volume of a cone
Volume = 1/3(area of base)(height)
sphere
the set of all points in space that are the same distance from a point, the center of the sphere.
hemispheres
a geometric plane passing through the center of a sphere divides it into two hemispheres
Surface area of a sphere
Surface area = 4(3.14)(radius)^2
Volume of a sphere
Volume = 4/3(3.14)(radius)^3
