Geometry Unit 8 Answers PHS
(L3) Use the midpoint formula, M=(x1+x22,y1+y22,z1+z22), to find the midpoint between the two points: (-3,3,0) and (0,0,5)
(-3/2,3/2,5/2)
(L1) Choose the correct net for the geometric solid. (cone)
110° angle (approx.) and circle
(L3) Leonhard Euler received his Master's degree at the age of _____.
16
(L3) Euler earned his Doctor's degree in mathematics and physics at age _____.
19
(L5) Find the lateral area of the cylinder using the lateral area formula: LA=2πrh.
20π in²
(L4) Find the surface area of the prism. (triangular prism; dimensions: 1.8cm, 1.8cm, 1.5cm, 2cm, 3.5cm)
22.6 cm²
(L4) Find the volume of the prism. (rectangular prism; dimensions : 2ft, 3ft, 4ft)
24 ft³
(L4) Find the lateral area of the prism using the formula LA=Ph. (rectangular prism; dimensions: 2.5cm, 3cm, 5cm)
40 cm²
(Q2) Find the volume of the cylinder. Use π=3.14 (slanted; r: 2.2 in; h: 3.5 in)
53.2 in³
(L5) Find the surface area of the cylinder using the formula SA=2πrh+2πr².
560πcm²
(L4) Find the surface area of the prism. (rectangular prism; dimensions: 2.5cm, 3cm, 4cm)
59 cm²
(L5) Find the volume of the cylinder using the formula V=πr²h. Use π=3.14. (slanted one)
602.9 in³
(L4) 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
(L5) Find the volume of the cylinder using the formula V=πr²h. Use π=3.14.
79,347.8 in³
(L3) 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
(L5) Find the surface area of the cylinder. Use π=3.14. Use the formulas LA=2πrh and SA=LA+2πr².
82.9 ft²
(Q2) Find the volume of the prism. (3 ft; 4 ft; 7 ft)
84 ft³
(L4) _____ 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
(L1) Complete the "family tree" of geometric solids. Geometric Solids: • __________ • Prism • __________ __________: • Cone • Cylinder • Sphere • __________
Complete the "family tree" of geometric solids. Geometric Solids: • Polyhedron • Prism • Pyramid Non-polyhedrons: • Cone • Cylinder • Sphere • Torus
(Q1) Determine if the shape is a polyhedron using Euler's formula. V-E=F Is it a polyhedron?
Determine if the shape is a polyhedron using Euler's formula. V-E=F 8 Is it a polyhedron? No
(L3) Determine if the shape is a polyhedron using Euler's formula. (triangular prism) V= __________ E= __________ F= __________ V-E+F= __________ Is it a polyhedron? __________
Determine if the shape is a polyhedron using Euler's formula. (triangular prism) V= 6 E= 9 F= 5 V-E+F= 2 Is it a polyhedron? Yes
(L3) Determine if the shape is a polyhedron using Euler's formula. (pentagonal pyramid) V= __________ E= __________ F= __________ V-E+F= __________ Is it a polyhedron? __________
Determine if the shape is a polyhedron using Euler's formula. (xxx) V= 6 E= 10 F= 6 V-E+F= 2 Is it a polyhedron? Yes
(L2) ______ is a sheet of paper with rows of dots that are arranged so they are oriented 30º from the horizontal.
Isometric dot paper
(L2) ______ 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
(L2) ______ 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
(Q1) Choose the correct solid for the net.
a box shape
(L1) Choose the correct net for the geometric solid. (circular prism)
a circle above and below a rectangle
(L1) Choose the correct net for the geometric solid. (hexagonal prism)
a hexagon with a smaller rectangle on each of its sides, with another hexagon connected to the other end of one of the rectangles.
(L5) 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
(L1) A _____ of a geometric solid is a face of a three-dimensional figure by which the figure is measured or classified.
base
(Q2) The curved surface that connects the two _____ of a cylinder is called the lateral surface of a cylinder.
bases
(L3) For all other triangles, the orthocenter, circumcenter and _____ are collinear.
centroid
(L3) In an isosceles triangle, the incenter, orthocenter, circumcenter, and centroid are _____.
collinear
(L1) A _____ is a geometric solid formed by a circular base and a curved surface that connects the base to a vertex.
cone
(L4) The _____ of a geometric solid is the intersection of a geometric solid with a plane.
cross section
(L1) A _____ is a rectangular prism with six square faces.
cube
(L1) A _____ is a geometric solid formed by two congruent, circular bases and a curved surface that connects the bases.
cylinder
(L1) The _____ of a geometric solid is the segment that is formed by the intersection of two faces of a three-dimensional figure.
edge
(Q1) 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
(Q1) A base of a geometric solid is a _____ of a three-dimensional figure by which the figure is measured or classified.
face
(L1) A _____ is a three-dimensional figure that encloses a region of space.
geometric solid
(L1) A face of a _____ is each flat surface of a three-dimensional figure.
geometric solid
(L2) The ______ is a horizontal line on a perspective drawing that contains the vanishing point or points.
horizon
(L2) Indicate whether the drawing is orthographic, isometric, or perspective. (a triangle shape)
isometric
(Q1) 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
(Q1) Indicate whether the drawing is orthographic, isometric, or perspective.
isometric
(L2) 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
(Q2) The _____ area is the sum of the areas of all of the lateral surfaces of a geometric solid.
lateral
(L4) The _____ is the sum of the areas of all of the lateral surfaces of a geometric solid.
lateral area
(L1) A(n) _____ is any face of a prism that is not a base.
lateral face
(L5) The curved surface that connects the two bases of a cylinder is called the _____ of a cylinder.
lateral surface
(L1) A _____ is a two-dimensional diagram of the surfaces of a three-dimensional figure that can be folded to form a geometric solid.
net
(Q1) 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
(L1) A _____ is a geometric solid that contains at least one curved surface.
non-polyhedron
(Q1) 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
(L1) A(n) _____ prism is a prism in which at least one of the lateral faces is not a rectangle.
oblique
(Q2) A(n) _____ cylinder is a cylinder in which its axis is not perpendicular to its bases.
oblique
(L5) An _____ is a cylinder in which its axis is not perpendicular to its bases.
oblique cylinder
(Q1) 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.
one
(L2) Determine whether the drawing is one point perspective or two point perspective. (Asian gates)
one point perspective
(L2) Determine whether the drawing is one point perspective or two point perspective. (shapes of R-E-S letters)
one point perspective
(Q1) Determine whether the drawing is one point perspective or two point perspective. (trail of squares, fading into the distance)
one point perspective
(L3) An _____ is a set of numbers that indicates the position of a point in space on a three-dimensional coordinate system.
ordered triple
(L2) A prospective home buyer wants to see an illustration showing all sides of the kitchen cabinets she wants to buy before they are installed.
orthographic
(L2) Indicate whether the drawing is orthographic, isometric, or perspective. (parts of a rectangle shape)
orthographic
(L2) 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
(Q1) Choose the correct solid for the net.
pentagonal triangle
(Q2) A right cylinder is a cylinder in which its axis is _____ to its bases.
perpendicular
(L2) An artist wants to produce a picture of a row of houses as observed from a point of view looking down the row.
perspective
(L2) Indicate whether the drawing is orthographic, isometric, or perspective. (circles)
perspective
(Q1) Indicate whether the drawing is orthographic, isometric, or perspective. (squares connected to form a line)
perspective
(Q1) 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
(L2) 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
(Q2) The cross section of a geometric solid is the intersection of a geometric solid with a(n) _____.
plane
(L1) A _____ is a geometric solid in which four or more polygons intersect only at their edges.
polyhedron
(L1) A _____ is a geometric solid formed by two parallel, congruent bases connected by faces that are parallelograms.
prism
(Q1) A lateral face is any face of a _____ that is not a base.
prism
(L3) 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
(L1) A _____ is a geometric solid formed by a polygonal base and triangular lateral faces that meet at a common vertex.
pyramid
(L3) Which graph shows both the projected points and the actual point for: (2,1,3) ?
pyramid-like shape on a coordinate plane (the bottom left coordinate is (3,-3,0))
(L5) A _____ is a cylinder in which its axis is perpendicular to its bases.
right cylinder
(L1) A _____ is a prism in which each lateral face is a rectangle.
right prism
(Q1) 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
(L1) A _____ is the locus of points in space that are a fixed distance from a point called the center of the sphere.
sphere
(Q2) The _____ area is the total area of all the faces and curved surfaces of a geometric solid.
surface
(L4) The total area of all the faces and curved surfaces of a geometric solid is called the _____.
surface area
(L3) Which graph shows the geometric solid with coordinates: (3,-3,0),(-3,3,0),(0,0,5),(-3,-3,0),(3,3,0)
tall and thin rectangle-like shape on a coordinate plane
(L3) In an equilateral triangle, the incenter, orthocenter, circumcenter, and centroid are _____.
the same point
(Q1) A geometric solid is a _____-dimensional figure that encloses a region of space.
three
(Q1) Choose the correct solid for the net.
triangular prism
(Q1) An ordered _____ is a set of numbers that indicates the position of a point in space on a three-dimensional coordinate system.
triple
(L2) Determine whether the drawing is one point perspective or two point perspective. (3D building drawing)
two point perspective
(Q1) Determine whether the drawing is one point perspective or two point perspective. (side angle of stacked rectangles)
two point perspective
(L1) Choose the correct net for the geometric solid. (pentagonal pyramid)
upside-down star shape
(Q1) A _____ point is a point on the horizon where nonvertical parallel lines appear to meet in a perspective drawing.
vanishing
(L2) A(n) ______ is a point on the horizon where nonvertical parallel lines appear to meet in a perspective drawing.
vanishing point
(L1) A _____ of a geometric solid is the point that is the intersection of three or more faces of a three dimensional figure.
vertex
(L4) 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