Math - Unit 8 - Solid Geometry
Use the midpoint formula, M=(x1+x22,y1+y22,z1+z22), to find the midpoint between the two points: (-3,30) and (0,0,5)
(-3/2, 3/2, 5/2)
-- Sorry, the I couldn't find the rest of the right answers for this assignment --
-- I'm also skipping the quiz because I don't know the right answers. I'm no good at math --
The _____ of a geometric solid is the intersection of a geometric solid with a plane.
cross section
A _____ is a cylinder in which its axis is perpendicular to its bases.
right cylinder
Determine whether the drawing is one point perspective or two point perspective
two point perspective
A(n) ____ is a point on the horizon where nonvertical parallel lines appear to meet in a perspective drawing.
vanishing point
The _____ of a geometric solid is the number of nonoverlapping unit cubes of a given size that will fill the interior of a geometric solid
volume
Find the volume of the prism.
24 ft^3
Find the volume of the cylinder using the formula V=πr2h.
79,347.8 in3
Use the distance formula d=(x2-x1)2+(y2-y1)2+(z2-z1)2 to find the distance between the two given points. (3, -3,0) and (-3,3,0)
8.5
Use π=3.14. Use the formulas LA=2πrh and SA=LA+2πr2.
82.9 ft2
Find the lateral area of the pyramid using the lateral area formula LA=12Pl.
84 ft2
Find the lateral area of the cone.
84π cm2
Find the volume of the cone.
8π ft3
The slant height is the distance from the apex of a cone to a point on the edge of the base.
Cylinder - no Pyramid - yes
The vertex is called an apex.
Cylinder - no Pyramid - yes
Determine if a property of a cone is similar to that of a cylinder or pyramid. The base is a circle.
Cylinder - yes Pyramid - no
The axis is not perpendicular to the base in an oblique cone.
Cylinder - yes Pyramid - no
The axis of a right cone is perpendicular to the base.
Cylinder - yes Pyramid - no
The lateral surface is a curved surface.
Cylinder - yes Pyramid - no
_____ is a sheet of paper with rows of dots that are arranged so they are oriented 30º from the horizontal.
Isometric dot paper.
A pyramid can be named according to the _____ of its base.
shape
Find the surface area of the sphere.
100π cm2
Find the surface area of the cone.
133π cm2
Leonhard Euler received his Master's degree at the age of _____.
16
Euler earned his Doctor's degree in mathematics and physics at age _____.
19
Find the lateral area of the cylinder using the lateral area formula: LA=2πrh.
20π in2
Find the surface area of the prism.
22.6 cm^2
Find the volume of the sphere.
288π ft3
Find the surface area of the regular pyramid.
3,157.56 in2
Find the surface area of the sphere.
36π m2
A pyramid has at least _____ vertices.
4
Find the lateral area of the prism using the formula LA=Ph.
40 cm^2 (cm squared)
Find the volume of the sphere.
4500π in3
Find the volume of the pyramid.
48 cm3
Find the surface area of the cylinder using the formula SA=2πrh+2πr2.
560π cm2
Find the surface area of the prism.
59 cm^2
Find the volume of the pyramid.
6 cm3
Find the volume of the cylinder using the formula V=πr2h. Use π=3.14.
602.9 in3
The volume of prism A is 630 in3. What is the volume of prism B if it is the same height as prism A and every cross sectional area of prism A is equal to every cross sectional area of prism B at the same level?
630 in^3
_____ principle states that if two geometric solids with the same height have the same cross-sectional area at every level, then they have the same volume.
Cavalieri's
A segment extends from the apex to the center of the base in a right cone.
Cylinder - no Pyramid - yes
The altitude is a segment that extends from the apex to the plane of its base and is perpendicular to the plane of the base.
Cylinder - no Pyramid - yes
A(n) _______ is a form of three-dimensional projection in which all three planes are drawn parallel to established axes and at full scale.
Isometric projection
The _____ of a cone is a segment that extends from the apex of a cone to the plane of its base and is perpendicular to the plane of the base.
altitude
The _____ of a pyramid is a segment that extends from the apex of a pyramid to the plane of its base and is perpendicular to the plane of the base.
altitude
The _____ is the vertex of a cone.
apex
The vertex opposite the base where all the lateral faces meet in a pyramid is called the _____.
apex
The _____ of a cone is a segment that extends from the apex of a cone to the center of the base
axis
The _____ of a cylinder is a segment that extends from one base of a cylinder to the other base and whose endpoints are the centers of the two bases.
axis
Mathematicians sometimes describe the inside space of a sphere as a _____.
ball
A sphere is different from other geometric solids in that it has no _____.
base
For all other triangles, the orthocenter, circumcenter and _____ are collinear.
centroid
If a plane intersects a sphere at a point other than a point of tangency, it forms a(n) _____.
circle
In an isosceles triangle, the incenter, orthocenter, circumcenter, and centroid are _____.
collinear
A _____ is a circle formed by the intersection of the surface of a sphere with a plane that passes through the center of the sphere
great circle
Half of a sphere is called a _____.
hemisphere
The ____ is a horizontal line on a perspective drawing that contains the vanishing point or points.
horizon
A pyramid whose base is not a regular polygon is a(n) _____ pyramid.
irregular
The lateral faces of a regular pyramid are all congruent _____ triangles.
isosceles
The _____ is the sum of the areas of all of the lateral surfaces of a geometric solid
lateral area
The _____ of a cone is the curved surface that connects the base of a cone to the apex of the cone
lateral surface
The curved surface that connects the two bases of a cylinder is called the _____ of a cylinder.
lateral surface
____ is a visual phenomenon in which the apparent size of objects with respect to their distance from the viewer are determined by means of intersecting lines that radiate from a point on the horizon.
linear perspective
A cone in which the axis of the cone is not perpendicular to the base is called a(n) _____ cone.
oblique
A(n) _____ pyramid is a pyramid in which the altitude of the pyramid extends from the apex to the plane of the base not at the center of the base.
oblique
An _____ is a cylinder in which its axis is not perpendicular to its bases.
oblique cylinder
Determine whether the drawing is one point perspective or two point perspective.
one point perspective
An _____ is a set of numbers that indicates the position of a point in space on a three-dimensional coordinate system.
ordered triple
Given the information, determine whether to use isometric, orthographic, or perspective drawing. A perspective home buyer wants to see an illustration showing all sides of the kitchen cabinets she wants to buy before they are installed.
orthographic
Indicate whether the drawing is orthographic, isometric, or perspective.
orthographic
A(n) _____ is a form of three-dimensional projection that presents six views of an object in which the line of sight for each view is perpendicular to the plane of the figure.
orthographic projection
Given the information, determine whether to use isometric, orthographic, or perspective drawing. An artist wants to produce a picture of a row of houses as observed from a point of view looking down the row.
perspective
Indicate whether the drawing is orthographic, isometric, or perspective.
perspective
A(n) _____ is a form of three-dimensional projection in which all nonvertical parallel lines appear to meet at a distant point, called the vanishing point.
perspective drawing
A(n) _____ is a point that lies on one of the three planes of a three-dimensional coordinate system and corresponds to two of the numbers in an ordered triple.
projected point
The _____ of a sphere is a segment that connects the center of the sphere with any point on the surface of the sphere.
radius
A(n) _____ pyramid is a right pyramid whose base is a regular polygon.
regular
A pyramid in which the altitude of the pyramid extends from the apex to the center of the base is called a(n) _____ pyramid.
right
A cone in which the axis of the cone is perpendicular to the base is called a(n) _____.
right cone
The _____ of a cone is the distance from the apex of a right cone to a point on the edge of the base.
slant height
The distance from the apex to the midpoint of an edge where a lateral face meets the base is called the _____ of a pyramid.
slant height
The total area of all the faces and curved surfaces of a geometric solid is called the _____.
surface area
In an equilateral triangle, the incenter, orthocenter, circumcenter, and centroid are _____.
the same point
_____ is a two dimensional representation of a three-dimensional figure drawn on a given plane as it would be seen from a particular direction or according to a particular set of rules.
three-dimensional projection