Geometry B unit 8

6) Find the surface area of the cylinder. Use π=3.14. Use the formulas LA=2πrh

37.1 ft2

6) Find the lateral area of the prism using the formula LA=Ph.

37.5 cm2

7) Find the surface area of the prism.

39 cm2

8) A pyramid has at least ___ vertices.

4

12) Determine if the shape is a polyhedron using Euler's formula.

V=6 E=9 F=5 V-E+F= Is it a polyhedron? yes

The segment of a geometric solid that is formed by the intersection of two faces of the three-dimensional figure is called a(n) _____.

edge

The slant height of a cone is the distance from the apex of a right cone to a point on the _____ of the base.

edge

Identify all the two-dimensional figures that are cross-sections for each of the three-dimensional solids.Right cone

ellipse circle triangle

The axis of a cylinder is a segment that extends from one base of a cylinder to the other base and whose _____ are the centers of the two bases.

endpoints

2) A face of a _____ is each flat surface of a three-dimensional figure.

geometric solid

The _____ of a sphere is a segment that connects the center of the sphere with any point on the surface of the sphere.

great

2) 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

1) Half of a sphere is called a ___.

hemisphere

Identify all the two-dimensional figures that are cross-sections for each of the three-dimensional solids.

oval circle rectangle

A right cylinder is a cylinder in which its axis is _____ to its bases.

perpendicular

11) Indicate whether the drawing is orthographic, isometric,or perspective.

perspective

16) 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

Linear _____ 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.

perspective

The cross section of a geometric solid is the intersection of a geometric solid with a(n) _____.

plane

14) A _____ is a geometric solid in which four or more polygons intersect only at their edges.

polyhedron

8) A _____ is a geometric solid formed by two parallel, congruent bases connected by faces that are parallelograms.

prism

A lateral face is any face of a _____ that is not a base.

prism

4) 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

11) A _____ is a geometric solid formed by a polygonal base and triangular lateral faces that meet at a common vertex.

pyramid

3) The ___ of a sphere is a segment that connects the center of the sphere with any point on the surface of the sphere.

radius

Identify all the two-dimensional figures that are cross-sections for each of the three-dimensional solids.Cube

rectangle triangle hexagon pentagon square

The rectangle below is rotated about the y-axis

rectangular prism with a radius of 5 and a height of 9

4) 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

3) A ___ is a cylinder in which its axis is perpendicular to its bases.

right cylinder

9) A _____ is a prism in which each lateral face is a rectangle.

right prism

9) A pyramid can be named according to the ___ of its base.

shape

6) 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

7) 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

10) A _____ is the locus of points in space that are a fixed distance from a point called the center of the sphere.

sphere

A circle centered at the origin is rotated about the y-axis

sphere

The _____ area is the total area of all the faces and curved surfaces of a geometric solid.

surface

4) The total area of all the faces and curved surfaces of a geometric solid is called the ___.

surface area

A projected point is a point that lies on _____ of the three planes of a three-dimensional coordinate system and corresponds to two of the numbers in an ordered triple.

the center

5) In an isosceles triangle, the incenter, orthocenter, circumcenter, and centroid are ___.

the same point

19) Choose the correct net for the geometric solid.

the star

10) Which graph shows both the projected points and the actual point for: (2,1,3)

the thin square

A geometric solid is a _____-dimensional figure that encloses a region of space.

three

Choose the correct solid for the net.

tringale

An ordered _____ is a set of numbers that indicates the position of a point in space on a three-dimensional coordinate system.

triple

14) Determine whether the drawing is one point perspective or two point perspective.

two point perspective

Determine whether the drawing is one point perspective or two point perspective.

two point perspective

A _____ point is a point on the horizon where nonvertical parallel lines appear to meet in a perspective drawing.

vanishing

1) A(n) ______ is a point on the horizon where nonvertical parallel lines appear to meet in a perspective drawing.

vanishing point

3) A _____ of a geometric solid is the point that is the intersection of three or more faces of a three dimensional figure.

vertex

The apex is the _____ of a cone.

vertex

2) 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

11) Determine if a property of a cone is similar to that of a cylinder or pyramid.

yes no yes yes yes no yes no yes yes yes yes no no no yes

Find the surface area of the cylinder.

12πcm2

9) Find the surface area of the cone.

133

Find the surface area of the cone.

1340

2) Euler earned his Doctor's degree in mathematics and physics at age ___.

19

9) Find the volume of the cylinder using the formula V=πr2h. Use π = 3.14.

192 in3

5) Find the lateral area of the cylinder using the lateral area formula: LA=2πrh

20in2

1) Leonhard Euler received his Master's degree at the age of ___.

21

8) Find the surface area of the prism.

22.6 cm2

Find the lateral area of the pyramid.

24

9) Find the volume of the prism.

24 ft3

Find the volume of the cone.

245

11) Find the lateral area of the pyramid using the lateral area formula LA=12Pl

28 ft2

10) Find the volume of the sphere.

288

Find the volume of the sphere.

288

8) Find the surface area of the sphere.

36

Find the volume of the cylinder. Use π=3.14

53.2 in3

The distance from the apex to the _____ of an edge where a lateral face meets the base is called the slant height of a pyramid.

midpoint

16) A _____ is a two-dimensional diagram of the surfaces of a three-dimensional figure that can be folded to form a geometric solid.

net

A(n) _____ cylinder is a cylinder in which its axis is not perpendicular to its bases.

oblique

13) Determine whether the drawing is one point perspective or two point perspective.

one point perspective

Determine whether the drawing is one point perspective or two point perspective.

one point perspective

2) The ______ is a horizontal line on a perspective drawing that contains the vanishing point or points.

perspective drawing

7) 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

18) Complete the "family tree" of geometric solids:

polyhedron pyramid non-polyhedron circle

2) A(n) ___ pyramid is a right pyramid whose base is a regular polygon.

regular

6) A cone in which the axis of the cone is perpendicular to the base is called a(n) ___.

right cone

An orthographic projection is a form of three-dimensional projection that presents _____ views of an object in which the line of sight for each view is perpendicular to the plane of the figure.

six

11) Which graph shows the geometric solid with coordinates:

the big triangle

20) Choose the correct net for the geometric solid.

the rectangle with a circle on top and bottom

3) 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

5) 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

1) The ___ is the vertex of a cone.

apex

The _____ of a cone is a segment that extends from the apex of a cone to the center of the base.

axis

5) Mathematicians sometimes describe the inside space of a sphere as a ___.

ball

A base of a geometric solid is a _____ of a three-dimensional figure by which the figure is measured or classified.

face

A pyramid has at least _____ vertices.

four

1) A _____ is a three-dimensional figure that encloses a region of space.

geometric solid

A(n) _____ circle 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

15) Given the information, determine whether to use isometric, orthographic, or perspective drawing. A prospective home buyer wants to see an illustration showing all sides of the kitchen cabinets she wants to buy before they are installed.

isometric

9) Indicate whether the drawing is orthographic, isometric,or perspective.

isometric

The _____ area is the sum of the areas of all of the lateral surfaces of a geometric solid.

lateral

The vertex opposite the base where all the _____ faces meet in a pyramid is called the apex.

lateral

1) The ___ is the sum of the areas of all of the lateral surfaces of a geometric solid.

lateral area

7) Find the surface area of the sphere.

100

9) Use the midpoint formula, M=(x1+x22,y1+y22,z1+z22), to find the midpoint between the two points:

(-32,32,52)/2

10) 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 in3

8) Find the volume of the cylinder using the formula V= π r2h.

79,347.8 in3

10) Find the volume of the cone.

8

8) Use the distance formula d=(x2-x1)2+(y2-y1)2+(z2-z1)2 to find the distance between the two given points.

8.5

Find the volume of the prism.

84 ft3

8) Find the lateral area of the cone.

84pi cm2

Find the surface area of the sphere.

900

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

4) ______ is a sheet of paper with rows of dots that are arranged so they are oriented 30º from the horizontal.

Isometric dot paper

8) ______ 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

Determine if the shape is a polyhedron using Euler's formula.

V-E+F=3 Is it a polyhedron? yes

1) A local company makes cement posts in the shape of the following three-dimensional composite.The cone and cylinder both have the same radius, while the height of the cylinder is 3 times the height of the cone. Which equation can be used to find the total volume of the cement post?

V=10/3πr2h

A circle is centered at the point (0,-2) and rotated about the x-axis

torus

Identify all the two-dimensional figures that are cross-sections for each of the three-dimensional solids.

trapezoid triangle square

Find the surface area of the prism.

36.8 cm2

Find the volume of the pyramid.

12

3) Randall built a scale model of a barn he wants to construct. What is the total volume of the model? Round your answers to the nearest tenth.

3,264.0 cm3

12) Find the surface area of the regular pyramid.

3054.24 in2

Find the lateral area of the cone.

45

9) Find the volume of the sphere.

4500

14) Find the volume of the pyramid.

48 cm3

2) A soccer ball with a diameter of 8.6 inches is shipped in a box that is a square prism and has a side length of 9.5 inches.How much volume is available to be filled with packing material if the shipping company wants the box completely full? Round your answer to the nearest tenth.

524.5 in3

7) Find the surface area of the cylinder using the formula SA=2πrh+2πr2

560π cm2

13) Find the volume of the pyramid.

6 cm3

Find the surface area of the pyramid.

6.75

13) Determine if the shape is a polyhedron using Euler's formula.

V=6 E=10 F=6 V-E+F=2 Is it a polyhedron? yes

3) ______ 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

The surface area of this cylinder is 12π cm2. What would happen to the surface area if the dimensions were doubled?

The surface area would remain at 12πcm2

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

1) The vertex opposite the base where all the lateral faces meet in a pyramid is called the ___.

apex

The altitude of a pyramid is a segment that extends from the _____ of a pyramid to the plane of its base and is perpendicular to the plane of the base.

apex

Cavalieri's principle states that if two geometric solids with the same height have the same cross-sectional _____ at every level, then they have the same volume.

area

2) The ___ of a cone is a segment that extends from the apex of a cone to the center of the base.

axis

2) 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

4) A sphere is different from other geometric solids in that it has no ___.

base

5) A _____ of a geometric solid is a face of a three-dimensional figure by which the figure is measured or classified.

base

The curved surface that connects the two _____ of a cylinder is called the lateral surface of a cylinder.

bases

7) For all other triangles, the orthocenter, circumcenter and ___ are collinear.

centroid

6) If a plane intersects a sphere at a point other than a point of tangency, it forms a(n) ___.

circle

Identify all the two-dimensional figures that are cross-sections for each of the three-dimensional solids.Sphere

circle

12) A _____ is a geometric solid formed by a circular base and a curved surface that connects the base to a vertex.

cone

The triangle below is rotated about the x-axis

cone with a radius of 8 and a height of 6

5) The ___ of a geometric solid is the intersection of a geometric solid with a plane.

cross section

6) A _____ is a rectangular prism with six square faces.

cube

Choose the correct solid for the net.

cube

The volume of a geometric solid is the number of nonoverlapping unit _____ of a given size that will fill the interior of a geometric solid.

cubes

The lateral surface of a cone is the _____ surface that connects the base of a cone to the apex of the cone.

curved

7) A _____ is a geometric solid formed by two congruent, circular bases and a curved surface that connects the bases.

cylinder

4) The _____ of a geometric solid is the segment that is formed by the intersection of two faces of a three-dimensional figure.

edge

5) A pyramid whose base is not a regular polygon is a(n) ___ pyramid.

irregular

A(n) _____ projection is a form of three-dimensional projection in which all three planes are drawn parallel to established axes and at full scale.

isometric

Indicate whether the drawing is orthographic, isometric, or perspective.

isometric

5) 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

10) The lateral faces of a regular pyramid are all congruent ___ triangles.

isosceles

The lateral faces of a regular pyramid are all congruent _____ triangles.

isosceles

17) A(n) _____ is any face of a prism that is not a base.

lateral face

1) The curved surface that connects the two bases of a cylinder is called the ___ of a cylinder.

lateral surface

4) The ___ of a cone is the curved surface that connects the base of a cone to the apex of the cone.

lateral surface

A two-dimensional diagram of the surfaces of a three-dimensional figure that can be folded to form a geometrical solid is called a _____.

net

13) A _____ is a geometric solid that contains at least one curved surface.

non-polyhedron

A perspective drawing is a form of three-dimensional projection in which all _____ parallel lines appear to meet at a distant point, called the vanishing point.

nonvertical

15) A(n) _____ prism is a prism in which at least one of the lateral faces is not a rectangle.

oblique

3) A cone in which the axis of the cone is not perpendicular to the base is called a(n) ___ cone.

oblique

7) 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

4) An ___ is a cylinder in which its axis is not perpendicular to its bases.

oblique cylinder

Choose the correct solid for the net.

octagons with triangle

6) In an equilateral triangle, the incenter, orthocenter, circumcenter, and centroid are ___.

on the same line

12) Determine whether the drawing is one point perspective or two point perspective.

one point perspective

3) An ___ is a set of numbers that indicates the position of a point in space on a three-dimensional coordinate system.

ordered triple

10) Indicate whether the drawing is orthographic, isometric,or perspective.

orthographic

6) 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