15. Three-Dimensional Geometry Flashcards
Prism
Volume?
Surface Area?
V = Bh
SA = Ph + 2B
B = base area, h = altitude, P = base perimeter
Rectangular Solid
Volume?
Surface Area?
V = lwh
SA = 2lw + 2lh + 2wh
l = length, w = width, h = altitude
Cube
Volume?
Surface Area?
V = s3
SA = 6s2
s = side length
Pyramid
Volume?
Surface Area?
V = 1/3 Bh
SA = 1/2 PL + B
B = base area, h = altitude, P = base perimeter, L = slant height
Cylinder
Volume?
Surface Area? (Lateral SA + Bases)
V = πr2h
SA = 2πrh + 2πr2
r = radius, h = altitude
Cone
Volume?
Surface Area? (Lateral SA + Base)
V = 1/3 πr2h
SA = πrL + πr2
r = radius, h = altitude, L = slant height = √( r2 + h2 )
Sphere
Volume?
Surface Area?
V = 4/3 πr3
SA = 4 πr2
r = radius
Length of a diagonal of a rectangular solid
√( l2 + w2 + h2 )
Distance between a point with coordinates (x1,y1,z1) and a plane with equation Ax + By + Cz + D = 0
Ax1 + By1 + Cz1 + D / √( A2 + B2 + C2 )
Point in a three-dimensional coordinate system
(x,y,z)
A point that has a zero coordinate…
A point that has two zero coordinates…
lies on the plane formed by the other two axes.
lies on the nonzero axis.
Distance between two points (x1,y1,z1) and (x2,y2,z2) in space
d = √[(x2–x1)2 + (y2–y1)2 + (z2–z1)2]
Equation of a sphere in space,
centered at (a, b, c) with raduis r
(x – a)2 + (y – b)2 + (z – c)2 = r2
