math 2: three-dimensional geometry *study Flashcards
on the level 2 test, all figures are assumed to b
right solids
prism volume
V = Bh,
where B is the base area
prism surface area
SA = Ph + 2B, where P is the base perimeter
rectangular solid volume
V = lwh
rectangular solid surface area
SA = 2lw + 2lh + 2wh
cube volume
V = s³
cube surface area
SA = 6s²
where s is the side length
pyramid volume
V = 1/3Bh
pyramid surface area
SA = 1/2 PL + B
where P is the base perimeter, L is the slant height
cylinder volume
V=πr²h
cylinder surface area
SA= 2πrh + 2πr²
cone volume
V= 1/3πr²h
cone surface area
SA= πrL + πr²
where L is the slant height
sphere volume
V = 4/3πr³
sphere surface area
SA = 4πr²
the formula for the length of a diagonal of a rectangular solid is D=
√l² + w² + h²
the coordinate plane an be extended by adding a third axis, the z-axis, whichis
perpendicular to the other two
a point that has zero as any coordinate must lie on the plane formbed by the
other two axes
if two coordinates of a point are zero, then the point lies on the
nonzero axis
distance between points (x1, y1, z1) and (x2, y2, z2):
d=√(x2 - x1)² + (y2 - y1)² + (z2 - z1)²
equation of a sphere exmple:
(x - 6)² + (y + 3)² + (z - 2)² = 36
if only two of the variables appear in an equation, the equation describes a
planar figure
the resulting three-dimensional figure is a solid that extends indefinitely in both directions parallel to the axis of the variale that is not in the equation, with cross sections
congruent to the planar figure
