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Level 624

Volume of Solids


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V = Bh
Volume of ANY prism
Volume of Cylinders
V = Bh
Volume of Cones
V = 1/3Bh
V = 1/3Bh
Volume of *Rectangular* Pyramids
polyhedron
a 3D solid with many faces
polygon
a closed figure made by joining line segments where each line segment intersects exactly 2 others
rotation
It is a transformation that turns a figure about a fixed point.
cross-section
cut it, pick it up and look where you cut... what shape do you see?
Apothem
The perpendicular distance from the center to a side of a regular polygon.
surface area
the total area of each surface or face added together
volume
measures the amount of space taken up by the object.
net
a 2-dimentional pattern that can be folded to make a 3-dimentional solid
pentagon
a 5 sided polygon
hexagon
a 6-sided polygon
heptagon
a 7-sided polygon
octagon
an 8-sided polygon
nonagon
a 9-sided polygon
decagon
a 10-sided polygon
½b(h)
area of a triangle
b(h)
Volume of a Prism
½(d₁)(d₂)
area of rhomubs or kite
½(h)(b₁+b₂)
area of a trapezoid
Πr²
Area of circle
SA of a Prism
SA = 2lw + 2lh + 2wh
Ph
Prism LA
LA+2B
Prism SA
bh
Prism V
1/2PL
Pyramid LA
LA+B
Pyramid SA
1/3Bh
Pyramid V
2πrh
LA of Cylinder
LA+2πr²
Cylinder SA
πr²h
V of cylinder
πrL
LA of Cone
LA+πr²
Cone SA
1/3πr²h
Cone V
4πr²
SA of Sphere
4/3πr³
V of Sphere
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.
cone
A solid shape with a circular base and a curved surface that come to a point (vertex).
pyramid
A solid shape with a polygon as a base and triangular faces that come to a point (vertex or apex)
V=4/3(pi)r3
Sphere (Volume)
S=4(pi)r2
Sphere (Surface Area)
faces
the faces of a polyhedron (polygons) that enclose a single region of space
edge of a polyhedron
a line segment formed by the intersection of two faces in a polyhedron
vertex of a polyhedron
a point where three or more edges meet
bases of a prism
congruent polygons in parallel planes
Euler's Theorem
The number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula F+V=E+2.
regular polyhedron
is a polyhedron with faces bounded by congruent regulaar polygons and with the same number of faces intersecting at each vertex.
convex polyhedron
any two points on its surface can be connected by a segment that lies entirely inside or on the polyhedron
concave polyhedron
if any two points on its surface are connected by a segment that goes outside the polyhedron
Platonic solids
regular tetrahedron (4 faces), cube (6 faces), regular octahedron (8 faces), regular dodecahedron (12 faces), regular icosahedron (20 faces)
regular tetrahedron
4 faces
cube
A solid shape that has: 6 square faces all equal in size, 8 vertices (corners), and 12 equal edges.
regular octahedron
8 faces
regular dodecahedron
12 faces
regular icosahedron
20 faces
cross section
the intersection of a plane and a solid
lateral faces
parallelograms formed by connecting the corresponding vertices of the bases (faces that aren't the bases)
lateral edges
the segments connecting the lateral faces
lateral area
the sum of the areas of its lateral faces
surface area of a prism
S = 2B + Ph
height of a prism
the perpendicular distance between its bases
right prism
each lateral edge is perpendicular to both bases
oblique prism
prism with lateral edges that are not perpendicular to its bases
height of a cylinder
the perpendicular distance between its bases
radius of a base
radius of the cylinder
right cylinder
the segment joining the centers of the bases is perpendicular to the bases
surface area of a cylinder
SA = 2 pi r squared + 2 pi r h