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Level 625

Volume of Solids II


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pyramid
A solid shape with a polygon as a base and triangular faces that come to a point (vertex or apex)
vertex of the pyramid
point where the triangles meet
regular pyramid
a pyramid that has a regular polygon for a base, the segment joining the vertex and the center of the base is perpendicular to the base
congruent isosceles triangles
lateral faces of a regular polygon
slant height of a regular pyramid
height of a lateral face of the regular pyramid
surface area of a pyramid
S = B + 1/2 PL
cone
A solid shape with a circular base and a curved surface that come to a point (vertex).
radius of the base
radius of the cone
height of a cone
the perpendicular distance between the vertex and the base
right cone
segment joining the vertex and the center of the base is perpendicular to the base and the slant height is the distance between the vertex and a point on the base edge
slant height of a cone
the distance between the vertex and a point on the base edge
lateral surface of a cone
consists of all segments that connect the vertex with points on the base edge
surface area of a right cone
The surface area S of a right cone is S=B=1/2Cl=╥r^2=╥rl, where B is the area of the base, C is the circumference of the base, r is the radius of the base, and l is the slant height.
volume of a solid
the number of cubic units contained in its interior
volume fo a cube postulate
the volume of a cube is the cube of the length of its sides
volume congruence postulate
if 2 polyhedra are congruent, then they have the same volume
volume addition postulate
the volume of a solid is the sum of the volumes of all its non-overlapping parts
Cavalieri's Principle Theorem
if two solids have the same height and the same cross-sectional area at every level, then they have the same volume
V = Bh
Volume of ANY prism
Volume of a Pyramid
V = 1/3 lwh
Volume of a Cone
V = 1/3 pi r squared h
sphere
A solid shape that is perfectly round like a ball. No faces, edges, or vertices.
center of a sphere
point equidistant from all points of a sphere
S = 4πr²
surface area of a sphere
Great Circle
when a plane intersects a sphere and the plane contains the center of the sphere
Hemispheres
the separate congruent halves divided by the great circle
volume of a sphere
V = 2/3 pi r squared h (or) V = 4/3 pi r cubed
similar solids
two solids of the same type with equal ratios of corresponding linear measures (like height or radii)
similar solids theorem
If two similar solids have a scale factor of a:b, then corresponding areas have a ratio of a ²:b ², and corresponding volumes have a ratio of a³:b³.
Prism LA
Pb x h
Prism TA
LA + 2Ab
Prism Volume
Ab x h
Pyramind LA
½ Pb x Hs
Pyramind TA
LA + Ab
Pyramind Volume
⅓ Ab x h
Cylinder LA
Cb x h
Cylinder TA
LA + 2Ab
Cylinder Volume
Ab x h
Cone LA
πr x Hs
Cone TA
LA + Ab
Cone Volume
⅓ Ab x h
4πr²
SA of Sphere
⁴⁄₃πr³
Sphere Volume
V=s³
volume of a cube
V=Bh
Prism: Volume
V=πr²h
Volume of a Circular Cylinder
Cavalieri's Principal Theorem
If two solids have the same height and the same cross-section area at every level, then they have the same volume
V= 1/3Bh
Volume of a pyramid
V=1/3πr²h
Volume of Cone
prism
A solid geometric figure whose two end faces are similar, equal and parallel rectilinear figures, and whose sides are parallelograms.
cylinder
A solid shape with one curved surface and two congruent circular bases.
cross section
the intersection of a plane and a solid
V=4/3 πr³
Volume of a Sphere
V=2/3πr³
Volume of a hemisphere
Volume- Pyramid
V=1/3 Bh
SA=2B+Ph
Surface Area- Prism
Volume- Cone
V= 1/3 Bh
V=πr^2h
Volume of a Cylinder
SA=2πr^2+2πrh
Surface Area- Cylinder
V=4/3πr^3
Volume of a Sphere
SA=4πr^2
Surface Area of a Sphere
A=1/2 aP
Area of a Hexagon
Circumference
2πr
Cavalieri's Principle
Same Base - Same Height - Volumes are the Same.
Variable B
Base area
Variable P
Perimeter of the base
Variable h
Height of the prism
Variable l
Slant height
Definition of apothem
A line from the center of a regular polygon at right angles to any of its sides.
a^2 + b^2 = c^2
used to check side lengths in a right triangle