math 2: three-dimensional geometry *study Flashcards

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1
Q

on the level 2 test, all figures are assumed to b

A

right solids

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2
Q

prism volume

A

V = Bh,

where B is the base area

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3
Q

prism surface area

A

SA = Ph + 2B, where P is the base perimeter

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4
Q

rectangular solid volume

A

V = lwh

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5
Q

rectangular solid surface area

A

SA = 2lw + 2lh + 2wh

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6
Q

cube volume

A

V = s³

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7
Q

cube surface area

A

SA = 6s²

where s is the side length

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8
Q

pyramid volume

A

V = 1/3Bh

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9
Q

pyramid surface area

A

SA = 1/2 PL + B

where P is the base perimeter, L is the slant height

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10
Q

cylinder volume

A

V=πr²h

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11
Q

cylinder surface area

A

SA= 2πrh + 2πr²

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12
Q

cone volume

A

V= 1/3πr²h

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13
Q

cone surface area

A

SA= πrL + πr²

where L is the slant height

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14
Q

sphere volume

A

V = 4/3πr³

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15
Q

sphere surface area

A

SA = 4πr²

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16
Q

the formula for the length of a diagonal of a rectangular solid is D=

A

√l² + w² + h²

17
Q

the coordinate plane an be extended by adding a third axis, the z-axis, whichis

A

perpendicular to the other two

18
Q

a point that has zero as any coordinate must lie on the plane formbed by the

A

other two axes

19
Q

if two coordinates of a point are zero, then the point lies on the

A

nonzero axis

20
Q

distance between points (x1, y1, z1) and (x2, y2, z2):

A

d=√(x2 - x1)² + (y2 - y1)² + (z2 - z1)²

21
Q

equation of a sphere exmple:

A

(x - 6)² + (y + 3)² + (z - 2)² = 36

22
Q

if only two of the variables appear in an equation, the equation describes a

A

planar figure

23
Q

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

A

congruent to the planar figure