Solid Mensuration Flashcards
A solid whose faces are plane polygons
Polyhedron
Polyhedra are named according to _________
number of faces
one that lies entirely on one side entirely on one side of a plane that contain any of its faces
Convex polyhedron
it contains at least one face so that there are parts of the polyhedron on both sides of a plane containing that face
Concave polyhedron
Polyhedron in three-dimensional spaces consist of?
Faces, edges and vertices
A solid with all its faces identical regular polygons
Regular polyhedron
It is constructed by congruent regular polygonal faces with the same number of faces meeting at each vertex
Platonic solids
Five platonic solids
tetrahedron, cube, octahedron, dodecahedron, or icosahedron
A polyhedron with two faces parallel and congruent and whose remaining faces are parallelograms
Prisms
A prism with all six faces a square.
Cube
Volume of a prism
V = abc
Surface area of a prism
A = 2(ab+bc+ca)
A prism which has its lateral faces perpendicular to the base
Right Prism
Volume of a Right Prism
V = Bh
Lateral Area of Right Prism
A = h x Pb Pb = perimeter of base
A Prism in which the lateral faces are not perpendicular to the base
Oblique Prism
Volume of a Oblique Prism
V = B x h = K x e K = area of a right section e = lateral edge
Lateral Area of a Oblique Prism
A = e x Pk e = lateral edge Pk = perimeter of right section
It is a portion of a prism contained between the base and a plane that is not parallel to the base
Truncated Prism
Volume of a Truncated Prism
V = B ( (h1 + h2 + h3 + h4) / 4 )
A solid bounded by a closed cylindrical surface and two parallel planes.
Cylinder
A cylinder which has its cylindrical surface perpendicular to the base
Right Cylinder
Volume a cylinder
V = B x h
Lateral area of a cylinder
A = (circumference of the base) x h
A cylinder which has its cylindrical surface not perpendicular to the base
Oblique Cylinder
Volume of a Oblique Cylinder
V = B x h = K x e K = Area of right section e = lateral edge
A polyhedron of which one face
Pyramid
Volume of pyramid
V = 1/3 x (B x H)
a portion of the pyramid included between the base and a section parallel to the base
Frustum of a pyramid
Volume of a Frustum of a pyramid
V = (h/3) x (B1 + B2 + sqrt(B1 x B2))
A solid bounded by a conical surface whose directrix is a closed curve and a plane which cuts all the elements
Cone
Volume of a cone
V = 1/3 (B x h)
a portion of the cone included between the base and a section parallel to the base
Frustum of a cone
Volume of a frustum of cone
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
Lateral area of a frustum of cone
A = pi (r + R) x S r = radius of upper base R = radius of lower base S = slant height of the frustum
Surface area of the frustum of cone
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
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
Prismatoid
Volume of the prismatoid
V = L/6 (A1 + 4 x Am + A2)
L = distance between end areas
A1 and A2 = end areas
Am = area at the midsection
a solid bounded by a closed surface every point of which is equidistant from a fixed point called center
Spheres
Volume of Sphere
V = 4/3 (pi x R^3)
Surface area of sphere
A = 4 x pi x R^2
Portion of the surface of a sphere included between two parallel planes
Zones
Area of Zone
A = 2 x pi x R x h
Solid bounded by a zone and the planes of the zone’s base
Spherical segment
Volume of spherical segment
V = (pi x h^2 / 3) (3R - h)
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
Spherical Sector
Volume of spherical sector
V = 1/3 (A x R) A = area of zone
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
Spherical pyramid
Volume of spherical pyramid
V = (pi x R^3 x E)/ 540 E = spherical excess of polygon ABCD in degress
a portion of a sphere bounded by two half great circles and an included arc.
Spherical wedges
Volume of spherical wedge
V = (pi x R^3 x theta) / 270
Solid formed by revolving a circle about a line not intersecting it
Torus
Volume of torus
V = 2 x pi^2 x R x r^2 R = distance from axis to center of generating circle r = radius of generating circle
Lateral area of torus
A = 4 x pi^2 x R x r R = distance from axis to center of generating circle r = radius of generating circle
A solid formed by revolving an ellipse about its axis
Ellipsoid
Volume of general ellipsoid
V = 4/3 (pi x a x b x c)
A solid formed by revolving an ellipse about its major axis
Prolate Spheroid
Volume of Prolate spheroid
V = 4/3 (pi x a x b^2)
A solid formed by revolving an ellipse about its minor axis
Oblate Spheroid
Volume of Oblate Spheroid
V = 4/3 (pi x a^2 x b)
A triangular pyramid
Tetrahedron
Refers to the positive height pyramid used in cumulation
Elavatum
Refers to the negative height pyramid used in cumulation
invaginatum
