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Bryx_Math > Solid Mensuration > Flashcards

Solid Mensuration Flashcards

1
Q

A solid whose faces are plane polygons

A

Polyhedron

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2
Q

Polyhedra are named according to _________

A

number of faces

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3
Q

one that lies entirely on one side entirely on one side of a plane that contain any of its faces

A

Convex polyhedron

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4
Q

it contains at least one face so that there are parts of the polyhedron on both sides of a plane containing that face

A

Concave polyhedron

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5
Q

Polyhedron in three-dimensional spaces consist of?

A

Faces, edges and vertices

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6
Q

A solid with all its faces identical regular polygons

A

Regular polyhedron

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7
Q

It is constructed by congruent regular polygonal faces with the same number of faces meeting at each vertex

A

Platonic solids

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8
Q

Five platonic solids

A

tetrahedron, cube, octahedron, dodecahedron, or icosahedron

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9
Q

A polyhedron with two faces parallel and congruent and whose remaining faces are parallelograms

A

Prisms

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10
Q

A prism with all six faces a square.

A

Cube

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11
Q

Volume of a prism

A

V = abc

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12
Q

Surface area of a prism

A

A = 2(ab+bc+ca)

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13
Q

A prism which has its lateral faces perpendicular to the base

A

Right Prism

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14
Q

Volume of a Right Prism

A

V = Bh

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15
Q

Lateral Area of Right Prism

A 
A = h x Pb
Pb = perimeter of base
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16
Q

A Prism in which the lateral faces are not perpendicular to the base

A

Oblique Prism

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17
Q

Volume of a Oblique Prism

A 
V = B x h = K x e
K = area of a right section
e = lateral edge
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18
Q

Lateral Area of a Oblique Prism

A 
A = e x Pk
e = lateral edge
Pk = perimeter of right section
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19
Q

It is a portion of a prism contained between the base and a plane that is not parallel to the base

A

Truncated Prism

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20
Q

Volume of a Truncated Prism

A

V = B ( (h1 + h2 + h3 + h4) / 4 )

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21
Q

A solid bounded by a closed cylindrical surface and two parallel planes.

A

Cylinder

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22
Q

A cylinder which has its cylindrical surface perpendicular to the base

A

Right Cylinder

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23
Q

Volume a cylinder

A

V = B x h

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24
Q

Lateral area of a cylinder

A

A = (circumference of the base) x h

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25
Q

A cylinder which has its cylindrical surface not perpendicular to the base

A

Oblique Cylinder

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26
Q

Volume of a Oblique Cylinder

A 
V = B x h = K x e
K = Area of right section
e = lateral edge
27
Q

A polyhedron of which one face

A

Pyramid

28
Q

Volume of pyramid

A

V = 1/3 x (B x H)

29
Q

a portion of the pyramid included between the base and a section parallel to the base

A

Frustum of a pyramid

30
Q

Volume of a Frustum of a pyramid

A

V = (h/3) x (B1 + B2 + sqrt(B1 x B2))

31
Q

A solid bounded by a conical surface whose directrix is a closed curve and a plane which cuts all the elements

A

Cone

32
Q

Volume of a cone

A

V = 1/3 (B x h)

33
Q

a portion of the cone included between the base and a section parallel to the base

A

Frustum of a cone

34
Q

Volume of a frustum of cone

A 
V = h/3 (B1 + B2 + sqrt(B1 x B2))
V = (pi x h)/3 (R^2 + r^2 + Rr)
R = radius of the lower base
r = radius of the upper base
35
Q

Lateral area of a frustum of cone

A 
A = pi (r + R) x S
r = radius of upper base
R = radius of lower base
S = slant height of the frustum
36
Q

Surface area of the frustum of cone

A 
A = pi ((r + R) x S) + pi x r^2 + pi x R^2
A = pi (r + R) x sqrt((R - r)^2 + h^2) + pi x r^2 + pi x R^2
R = radius of lower base
r = radius of upper base
S = slant height of the frustum
37
Q

A polyhedron having for bases two polygons in parallel planes and for lateral faces triangles or trapezoids with one side lying in one bae, and the opposite vertex or side lying in the other base of the polyhedron

A

Prismatoid

38
Q

Volume of the prismatoid

A

V = L/6 (A1 + 4 x Am + A2)
L = distance between end areas
A1 and A2 = end areas
Am = area at the midsection

39
Q

a solid bounded by a closed surface every point of which is equidistant from a fixed point called center

A

Spheres

40
Q

Volume of Sphere

A

V = 4/3 (pi x R^3)

41
Q

Surface area of sphere

A

A = 4 x pi x R^2

42
Q

Portion of the surface of a sphere included between two parallel planes

A

Zones

43
Q

Area of Zone

A

A = 2 x pi x R x h

44
Q

Solid bounded by a zone and the planes of the zone’s base

A

Spherical segment

45
Q

Volume of spherical segment

A

V = (pi x h^2 / 3) (3R - h)

46
Q

Solid generated by rotating a sector of a circle about an axis which passes through the center of the circle but which contains no point inside the sector

A

Spherical Sector

47
Q

Volume of spherical sector

A 
V = 1/3 (A x R)
A = area of zone
48
Q

a pyramid formed by a portion of a sphere as base and whose elements are the edges from the vertices of the base to the center of the sphere

A

Spherical pyramid

49
Q

Volume of spherical pyramid

A 
V = (pi x R^3 x E)/ 540
E = spherical excess of polygon ABCD in degress
50
Q

a portion of a sphere bounded by two half great circles and an included arc.

A

Spherical wedges

51
Q

Volume of spherical wedge

A

V = (pi x R^3 x theta) / 270

52
Q

Solid formed by revolving a circle about a line not intersecting it

A

Torus

53
Q

Volume of torus

A 
V = 2 x pi^2 x R x r^2
R = distance from axis to center of generating circle
r = radius of generating circle
54
Q

Lateral area of torus

A 
A = 4 x pi^2 x R x r
R = distance from axis to center of generating circle
r = radius of generating circle
55
Q

A solid formed by revolving an ellipse about its axis

A

Ellipsoid

56
Q

Volume of general ellipsoid

A

V = 4/3 (pi x a x b x c)

57
Q

A solid formed by revolving an ellipse about its major axis

A

Prolate Spheroid

58
Q

Volume of Prolate spheroid

A

V = 4/3 (pi x a x b^2)

59
Q

A solid formed by revolving an ellipse about its minor axis

A

Oblate Spheroid

60
Q

Volume of Oblate Spheroid

A

V = 4/3 (pi x a^2 x b)

61
Q

A triangular pyramid

A

Tetrahedron

62
Q

Refers to the positive height pyramid used in cumulation

A

Elavatum

63
Q

Refers to the negative height pyramid used in cumulation

A

invaginatum

Bryx_Math (9 decks)

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