Solid Mensuration

Question 1

A solid whose faces are plane polygons

Answer 1

Polyhedron

Question 2

Polyhedra are named according to _________

Answer 2

number of faces

Question 3

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

Answer 3

Convex polyhedron

Question 4

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

Answer 4

Concave polyhedron

Question 5

Polyhedron in three-dimensional spaces consist of?

Answer 5

Faces, edges and vertices

Question 6

A solid with all its faces identical regular polygons

Answer 6

Regular polyhedron

Question 7

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

Answer 7

Platonic solids

Question 8

Five platonic solids

Answer 8

tetrahedron, cube, octahedron, dodecahedron, or icosahedron

Question 9

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

Answer 9

Prisms

Question 10

A prism with all six faces a square.

Answer 10

Cube

Question 11

Volume of a prism

Answer 11

V = abc

Question 12

Surface area of a prism

Answer 12

A = 2(ab+bc+ca)

Question 13

A prism which has its lateral faces perpendicular to the base

Answer 13

Right Prism

Question 14

Volume of a Right Prism

Answer 14

V = Bh

Question 15

Lateral Area of Right Prism

Answer 15

A = h x Pb
Pb = perimeter of base

Question 16

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

Answer 16

Oblique Prism

Question 17

Volume of a Oblique Prism

Answer 17

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

Question 18

Lateral Area of a Oblique Prism

Answer 18

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

Question 19

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

Answer 19

Truncated Prism

Question 20

Volume of a Truncated Prism

Answer 20

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

Question 21

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

Answer 21

Cylinder

Question 22

A cylinder which has its cylindrical surface perpendicular to the base

Answer 22

Right Cylinder

Question 23

Volume a cylinder

Answer 23

V = B x h

Question 24

Lateral area of a cylinder

Answer 24

A = (circumference of the base) x h

Question 25

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

Answer 25

Oblique Cylinder

Question 26

Volume of a Oblique Cylinder

Answer 26

``` V = B x h = K x e K = Area of right section e = lateral edge ```

Question 27

A polyhedron of which one face

Answer 27

Pyramid

Question 28

Volume of pyramid

Answer 28

V = 1/3 x (B x H)

Question 29

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

Answer 29

Frustum of a pyramid

Question 30

Volume of a Frustum of a pyramid

Answer 30

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

Question 31

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

Answer 31

Cone

Question 32

Volume of a cone

Answer 32

V = 1/3 (B x h)

Question 33

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

Answer 33

Frustum of a cone

Question 34

Volume of a frustum of cone

Answer 34

``` 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 ```

Question 35

Lateral area of a frustum of cone

Answer 35

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

Question 36

Surface area of the frustum of cone

Answer 36

``` 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 ```

Question 37

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

Answer 37

Prismatoid

Question 38

Volume of the prismatoid

Answer 38

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

Question 39

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

Answer 39

Spheres

Question 40

Volume of Sphere

Answer 40

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

Question 41

Surface area of sphere

Answer 41

A = 4 x pi x R^2

Question 42

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

Answer 42

Zones

Question 43

Area of Zone

Answer 43

A = 2 x pi x R x h

Question 44

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

Answer 44

Spherical segment

Question 45

Volume of spherical segment

Answer 45

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

Question 46

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

Answer 46

Spherical Sector

Question 47

Volume of spherical sector

Answer 47

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

Question 48

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

Answer 48

Spherical pyramid

Question 49

Volume of spherical pyramid

Answer 49

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

Question 50

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

Answer 50

Spherical wedges

Question 51

Volume of spherical wedge

Answer 51

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

Question 52

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

Answer 52

Torus

Question 53

Volume of torus

Answer 53

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

Question 54

Lateral area of torus

Answer 54

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

Question 55

A solid formed by revolving an ellipse about its axis

Answer 55

Ellipsoid

Question 56

Volume of general ellipsoid

Answer 56

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

Question 57

A solid formed by revolving an ellipse about its major axis

Answer 57

Prolate Spheroid

Question 58

Volume of Prolate spheroid

Answer 58

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

Question 59

A solid formed by revolving an ellipse about its minor axis

Answer 59

Oblate Spheroid

Question 60

Volume of Oblate Spheroid

Answer 60

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

Question 61

A triangular pyramid

Answer 61

Tetrahedron

Question 62

Refers to the positive height pyramid used in cumulation

Answer 62

Elavatum

Question 63

Refers to the negative height pyramid used in cumulation

Answer 63

invaginatum