Surface Area and Volume
Drawing 3-D Figures
Class Work
1. For each of the following name the edges, faces, and vertices.
a.
b.
c.
2. For each shape name the lateral edges and base edges.
a.
b.
c.
3. Consider the figure in question 2a. How many vertices, edges, and faces does it have?
What does V – E + F= ? Do the same for 2b., does V – E + F= the same thing?
Homework
4. For each of the following the name edges, faces, and vertices.
a.
b.
c.
5. For each shape name the lateral faces and base(s).
a.
b.
c.
6. Consider the figure in question 5a. How many vertices, edges, and faces does it have?
What does V – E + F= ? Do the same for 5b., does V – E + F= the same thing?
Surface v. Volume
Class Work
Describe the following objects as a solid or a surface.
7. Beach ball
8. Dime
9. Shoebox
10. Draw the cross-section indicated
a.
b.
c
11. Describe the cross-section of a hexagonal prism given that the plane of intersection is
a. Between and parallel to the bases
b. Contains corresponding diagonals of the bases
c. Intersects all of the faces
Homework
Describe the following objects as a solid or a surface.
12. Recycled can
13. Brick
14. Golfball
15. Draw the cross-section indicated
a.
b.
c.
16. Describe the cross-sections of a cone given the that the plane of intersection is
a. Parallel to the base
b. Oblique to the base but not intersecting the base
c. Intersects the base at 2 points
Right v. Oblique
Class Work
17. State the name of the surface.
a.
d.
b.
c.
e.
f.
18. Draw a right hexagonal pyramid surface.
19. Draw an oblique conical solid.
Homework
20. State the name of the surface.
a.
b.
d.
c.
e.
21. Draw a right cylindrical solid.
22. Draw an oblique square prism surface.
Nets
Class Work
Draw the figure and the net of the following surfaces.
23. A right square prism
24. An oblique cylinder
25. A right cone
26. A right pentagonal pyramid
27. Use the net of the right triangular prism to find x.
Homework
Draw the figure and the net of the following surfaces.
28. An oblique triangular prism
29. An right cylinder
30. An oblique cone
31. A right octagonal pyramid
32. Use the net of the right hexagonal pyramid to find x.
Views
Class Work
33. Sketch the front, left, and top of the figure.
a.
b.
34. Draw the solid given the top, left, and front views
a.
b.
Homework
35. Sketch the front, left, and top of the solid.
a.
b.
36. Draw the solid given the top, left, and front views
a.
b.
Surface Area of a Prism
Class Work
37.
A jewelry store buys small boxes in which to wrap items that they sell. The diagram
below shows one of the boxes. Find the lateral area and the surface area of the box to the
nearest whole number.
38. Find the lateral area and surface area of the hexagonal prisms.
39. Find the surface area of the composite space figure.
40. Consider the prism shown below.
a.
Draw a net for the prism and label all dimensions.
b.
Use the net to find the surface area of the prism.
41. Find the lateral area and surface area of the triangular prism.
a.
b.
c.
Homework
42. Draw the net and label all of the dimensions for the prism. Find the lateral area and surface
area of the rectangular prism.
43. Find the lateral area and surface area of the regular pentagonal prism.
44. Find the surface area of the composite space figure.
A 5x6x8 box with a triangular prism removed.
(Triangle is equilateral)
a
45. Find the lateral area and surface area of the triangular prisms.
b.
Surface Area of a Cylinder
Class Work
46. The radius of the base of a cylinder is 39 in. and its height is 33 in.. Find the surface area of
the cylinder in terms of  .
47. Andrew is planning to cover the lateral surface of a large cylindrical garbage can with
decorative fabric for a theme party. The can has a diameter of 3 feet and a height of 3.5
feet. How much fabric does he need if he covers the lid but not the bottom of the can?
48. Find the lateral Area and Surface Area of the Cylinder
49. Jalissa wants to paint just the sides of a cylindrical pottery vase that has a height of 35 cm
and a diameter of 12 cm. Find the number of square centimeters she will need to paint.
Explain the method you would use to find the lateral area.
50. Find the surface area of the composite figure.
51. A washer is a cylindrical solid with a smaller cylinder removed from the center and then
dipped in a special coating. If the diameter of the washer is 4”, the diameter of the hole is
1“, and height ¼ “, find the surface area of the washer.
Homework
52. Andrew is planning to cover the lateral surface of a large cylindrical swimming pool with
decorative fabric for a theme party. The pool has a radius of 9 feet and a height of 4 feet.
How much fabric does he need?
53. Find the lateral Area and Surface Area of the Cylinder
a
b.
54. Jasmin wants to paint just the sides of a cylindrical pottery vase that has a height of 48 cm
and a diameter of 19 cm. Find the number of square centimeters she will need to paint.
55. Find the surface area for the composite figure.
56. A washer is a cylindrical solid with a smaller cylinder removed from the center and then
dipped in a special coating. If the diameter of the washer is 3”, the diameter of the hole is
½“, and height is ¼ “, find the surface area of the washer.
Surface Area of a Pyramid
Class Work
57. Find the surface area of the pyramid.
58. Find the slant height, lateral area and surface area of the pyramid.
59. Find the slant height, lateral area and surface area of each square pyramid.
a.
b.
60. Find the surface area of the composite figure.
61. A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length of
15 cm, a width of 5 cm, and a height of 7 cm. The pyramid has a height of 13 cm. Find the
surface area of the composite figure.
Homework
62. A regular hexagonal pyramid has base edges of 48 cm and a slant height of 26 cm. Find
the lateral area and surface area.
63. Find the slant height, lateral area and surface area of each square pyramid.
a.
b.
64. Find the Surface Area of the composite figure.
Surface Area of a Cone
Class Work
65. Find the slant height of the cone.
66. Find the surface area of the cone in terms of  .
a.
b.
67. Find the surface area of a conical grain storage tank that has a height of 30 meters and a
diameter of 14 meters.
68. The lateral area of a right cone is 40𝜋 ft2, find the height of the cone if slant height is 10ft.
69. The surface area of a right cone is 55𝜋 cm2, find the radius if the slant height is 6cm.
Homework
70. Find the slant height of the cone with height 7 and radius 6.
71. Find the lateral Area and surface Area of the cone.
a.
b.
72. The lateral area of a cone is 558 cm2. The radius is 31 cm. Find the slant height.
73. The lateral area of a right cone is 30𝜋 ft2, find the height of the cone if slant height is 8ft.
74. The surface area of a right cone is 30𝜋 cm2, find the radius if the slant height is 7cm.
Spheres
Class Work
75. The equator of Earth is approximately 25,000 miles. What is the diameter of the Earth?
76. The cross section of a sphere taken 4 units from the center of the sphere has radius 6.
What is the radius of the sphere?
77. The cross section of a sphere taken 7 units from the center of the sphere has an area of
9𝜋u2. What is the radius of the sphere?
78. A new dome-shaped storage shed is a hemisphere with height 10 yds. What is the area of
the floor space?
79. A basketball has a circumference of 28”, what is the diameter of the ball?
Homework
80. The diameter of Jupiter is approximately 89,000 miles. How long is Jupiter’s equator?
81. The cross section of a sphere taken 8 units from the center of the sphere has radius 7.
What is the radius of the sphere?
82. The cross section of a sphere taken 5 units from the center of the sphere has an area of 6u2.
What is the radius of the sphere?
83. A new dome-shaped storage shed is a hemisphere with height 8 yds. What is the area of
the floor space?
84. A baseball has a circumference of 9”, what is the diameter of the ball?
Surface Area of a Sphere
Class Work
85. Find the surface area of the sphere with the given dimension.
a. Radius = 60 m
b. Diameter = 24 cm
c. Circumference = 13 mm
86. Find the surface area of a sphere that has a great circle with circumference of 13 mm.
Round to the nearest tenth.
87. A balloon has a surface area of 200 cm2. Find the radius of the balloon.
88. Find the surface area of the sphere.
a.
b.
89. Three balls are packaged in a cylindrical container as shown below. The balls just touch the
a.
b.
c.
top, bottom, and sides of the cylinder. The diameter of each ball is 7 cm.
What is the radius of the cylinder?
What is the height of the cylinder?
What is the total surface area of the three balls?
Homework
90. Find the surface area of the sphere with the given dimension. Leave your answer in terms of
.
a. Radius = 45 m
b. Diameter = 16 cm
c. Circumference = 27 mm
91. A ball has a surface area of 35.5 cm2. Find its radius.
92. Find the surface area of the sphere.
a.
b.
93. Three balls are packaged in a cylindrical container as shown below. The balls just touch the
top, bottom, and sides of the cylinder. The diameter of each ball is 9 cm.
a. What is the radius of the cylinder?
b. What is the height of the cylinder?
c. What is the total surface area of the three balls?
Volume of Prisms
Class Work
94. Concrete can be purchased by the cubic yard. How much will it cost to pour a slab 18 feet
by 18 feet by 4 inches for a patio if the concrete costs $41.00 per cubic yard?
95. Find the volume of the rectangular prism
a.
b.
96. Find the volume of the triangular prism
a.
b.
97. Find the volume.
a.
c.
b.
Homework
98. A jewelry store buys small boxes in which to wrap items that they sell. The diagram below
shows one of the boxes. Find the volume of the box.
99. Find the volume of the Rectangular Prisms
100.
Find the volume of the box w/ triangular prism removed.
101. Find the volume of the Triangular Prism
a.
b.
102.
Find the volume.
Volume of Cylinders
Class Work
103. The radius of the base of a cylinder is 39 in. and its height is 33 in. Find the volume of
the cylinder.
104. Denise wants to use a cylindrical garbage can for recycling. The can has a diameter of
4 feet and a height of 2.5 feet. How many cubic feet of recycling will fit into the garbage can?
105. A washer is a cylindrical solid with a smaller cylinder removed from the center. If the
diameter of the washer is 3”, the diameter of the hole is ½”, and height ¼ “, find the volume
of the washer.
106. A cylinder has a volume of 271.4 cubic inches and a base diameter of 12 in. Find the
height of the cylinder.
107.
Find the volume of the cylinder.
108.
Find the volume of the composite figure.
Homework
109. Denise is going to a pot luck dinner party and needs to use a cylindrical container for her
potato salad. The container has a diameter of 15 inches and a height of 7 inches. How many
cubic inches of potato salad can Denise fit into the container to take to the pot luck dinner?
110. A washer is a cylindrical solid with a smaller cylinder removed from the center. If the
diameter of the washer is 4” and the diameter of the hole is 1“, and height ¼ “, find the
volume of the washer.
111. Find the volume of the cylinder.
a.
b.
112.
Find the volume of the composite figure.
Volume of Pyramids
Class Work
113. Find the volume of the pyramid.
a.
114.
b.
Find the volume of the composite figure.
115. A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length
of 15 cm, a width of 5 cm, and a height of 7 cm. The pyramid has a height of 13 cm. Find the
volume of the composite figure.
Homework
116. A square pyramid has base edges of 48 cm and a slant height of 26 cm. Find its
volume.
117. Find the volume of the pyramid.
a.
b.
118.
Find the volume of the composite figure.
119. A rectangular pyramid fits exactly on top of a rectangular prism. The prism has a length
of 12 cm, a width of 6 cm, and a height of 8 cm. The pyramid has a height of 10 cm. Find the
volume of the composite figure.
Volume of Cones
Class Work
120. Find the volume of the cone in terms of  .
a.
b.
c.
121. A conical grain storage tank has a height of 30 meters and a diameter of 14 meters. Find
the capacity of the storage tank. Round the answer to the nearest square meter.
122. If a cone has height 6 ft and volume 54 ft3, find the radius of the base.
123. The vertex of a right cone has a 20o angle and the slant height is 10 cm. Find the volume
of the cone.
Homework
124. The lateral area of a cone is 558 cm2. The radius is 5 cm. Find the volume of the cone
to the nearest tenth.
125.
Find the volume of the cone.
126.
If a cone has height 9 ft and volume 75 ft3, find the radius of the base.
127. The vertex of a right cone has a 40o angle and the slant height is 12 cm. Find the volume
of the cone.
Volume of a Sphere
Class Work
128. Find the volume of the sphere with the given dimension. Leave your answer in terms of
.
a. Radius = 60 m
b. Diameter = 14 cm
c. Circumference = 13 mm
129.
A balloon has a surface area of 200 cm2. Find the volume of the balloon.
130. Find the volume of the sphere.
a.
b.
131. Three balls are packaged in a cylindrical container as shown below. The balls just touch
the top, bottom, and sides of the cylinder. The diameter of each ball is 7 cm.
a.
b.
c.
What is the volume of the cylinder? Explain your method for finding the volume.
What is the total volume of the three balls? Explain your method for finding the
total volume.
What percent of the volume of the container is occupied by the three balls?
Explain how you would find the percent.
Homework
132. Find the volume of the sphere with the given dimension. Leave your answer in terms of .
a. Radius = 45 m
133.
b. Diameter = 16 cm
A ball has a volume of 15.5 cm3. Find the ball’s surface area.
134. Find the volume of the sphere.
a.
c. Circumference = 27 mm
b.
135. Three balls are packaged in a cylindrical container as shown below. The balls just touch
the top, bottom, and sides of the cylinder. The diameter of each ball is 13 cm.
a.
What is the volume of the cylinder? Explain your method for finding the volume.
b.
What is the total volume of the three balls? Explain your method for finding the
total volume.
c.
What percent of the volume of the container is occupied by the three balls?
Explain how you would find the percent.
Cavalieri’s Principle
Class Work
136. The following solids have the same volumes. Find x.
a.
b.
137. Determine whether Cavalieri’s can be used to compare the volumes of any of the solids.
Explain your reasoning.
Homework
138. The following solids have the same volumes. Find x.
a.
b.
139. Determine whether Cavalieri’s can be used to compare the volumes of any of the solids.
Explain your reasoning.
Corresponding Parts of Similar Solids
Class Work
140. Determine whether each pair of solids is similar or not. If similar, find the ratio of
similitude.
a.
b.
141.
142.
143.
The ratio of the slant heights of 2 similar pyramids is 2 to 5.
a. What is the ratio of their heights?
b. What is the ratio of their surface areas?
c. What is the ratio of their volumes?
The ratio of surface areas of 2 similar solids is 16 to 9.
a. What is the ratio of their heights?
b. What is the ratio of their lateral areas?
c. What is the ratio of their volumes?
The ratio of surface areas of 2 similar solids is 8 to 1.
a. What is the ratio of their heights?
b. What is the ratio of the area of their bases?
c. What is the ratio of their weights (made of the same materials)?
Homework
144. Determine whether each pair of solids is similar or not. If similar, find the ratio of
similitude.
a.
b.
145.
146.
147.
The ratio of the slant heights of 2 similar cones is 6 to 7.
a. What is the ratio of their radii?
b. What is the ratio of their surface areas?
c. What is the ratio of their volumes?
The ratio of surface areas of 2 similar solids is 25 to 4.
a. What is the ratio of their heights?
b. What is the ratio of their lateral areas?
c. What is the ratio of their volumes?
The ratio of surface areas of 2 similar solids is 27 to 125.
a. What is the ratio of their heights?
b. What is the ratio of the area of their bases?
c. What is the ratio of their weights (made of the same materials)?
Coordinates in Space
Class Work
148. Graph the points A(2,1,4), B(-2,0, -5), and C(0,4,0).
149. What is the distance between (1,2,3) and (4,5,6)?
150. What is the distance between (-4,0,-7) and (3,-2,-9)?
151. How far is (5,3,-4) from the origin?
152. What is the length of a diagonal of a box with sides 4x4x8?
153. What is the length of a diagonal of a box with sides 2x3x6?
154. What is radius and the center of the sphere with equation: (x-2)2 + y2 + (z-4)2= 36?
155. What is radius and the center of the sphere with equation: x2 + 6x+ y2 + (z-7)2= 16?
156. What is radius and the center of the sphere with equation: x2 - 6x+ y2 +8y+ z2 -10z= -1?
157. Is the point (0, -1, 0) inside, on, or outside of (x-2)2 + (y+5)2 + (z-4)2= 36?
158. Name a point on (x-2)2 + (y+7)2 + (z-4)2= 36.
Homework
159. Graph the points A(4,-2,3), B(0, -2, -3), and C(0,0,5).
160. What is the distance between (10,6,2) and (3,5,7)?
161. What is the distance between (-2,1,-5) and (4,-6,-3)?
162. How far is (-5,-3,-4) from the origin?
163. What is the length of a diagonal of a box with sides 5x7x6?
164. What is the length of a diagonal of a box with sides 1x2x3?
165. What is radius and the center of the sphere with equation: (x+3)2 + y2 + (z+5)2= 64?
166. What is radius and the center of the sphere with equation: x2 + 12x+ y2 + (z-8)2= -16?
167. What is radius and the center of the sphere with equation: x2 - 10x+ y2 +4y+ z2 +20z=15?
168. Is the point (-4, 1, 3) inside, on, or outside of (x+3)2 + y2 + (z+5)2= 64?
169. Name a point on (x-5)2 + y2 + (z+3)2= 49.
Multiple Choice
1. A right square pyramid has base edges of 6 and a height of 5. Find the slant height.
a. 3.3
b. 4
c. 5.8
d. 7.8
2. How many base edges does an oblique hexagonal prism have?
a. 6
b. 7
c. 12
d. 14
3. The views of a solid made of cubes are given. If the length of an edge of the cube is 2, what
is the total volume of the solid?
a. 10 u3
b. 20 u3
c. 30 u3
d. 40 u3
4. Find the lateral area of the right regular pyramid represented by the net.
a. 120 u2
b. 60 u2
c. 48 u2
d. 24 u2
5. The surface area of a box with length 5 cm and width 4 cm is 76 cm2. Find the height.
a. 2 cm
b. 3.8 cm
c. 4 cm
d. 5 cm
6. Find the surface area of a right cone with radius 3 and slant height 4.
a. 12𝜋 𝑢2
b. 15𝜋 𝑢2
c. 21𝜋 𝑢2
d. 24𝜋 𝑢2
7. A cross-section of a sphere, which is 6 units form the center of the sphere, has a
circumference of 8𝜋 units. Find the surface area of the sphere.
a. 52𝜋 𝑢2
b. 144𝜋 𝑢2
c. 208𝜋 𝑢2
d. 400𝜋 𝑢2
8. Find the volume of the right triangular prism.
a. 60 u3
b. 100 u3
c. 120 u3
d. 200 u3
9. Find the volume of the cylinder with height 6 ft and radius 4 ft.
a. 32𝜋 𝑓𝑡 3
b. 48𝜋 𝑓𝑡 3
c. 96𝜋 𝑓𝑡 3
d. 144𝜋 𝑓𝑡 3
10. Find the volume of the right square pyramid with base edges of 8 and slant height of 10.
a. 586.6 u3
b. 384 u3
c. 195.5 u3
d. 128 u3
11. The surface areas of 2 similar spheres have the ratio of 9 to 4. If the volume of the larger
sphere is 405 u3, what is the volume of the smaller sphere?
a. 120 u3
b. 160 u3
c. 180 u3
d. 270 u3
12. Find the length of a diagonal of a box with sides 12 mm , 16 mm, and 4 cm
a. 20.4 mm
b. 27.7 mm
c. 44.7 mm
d. 87.6 mm
13. Which of the following points is on the sphere (x-2)2 + y2 + (z+4)2 = 36?
a. (2, 0, 4)
b. (-2, 0, -4)
c. (2, 6, -4)
d. (5, 4, 1)
Extended Response
1. A surface is a composition of a right cylinder and a right cone as shown. The cone has a
slant height of 10’ and radius 6’.
a. Find the height of the cone.
b. If cone has the same height as the cylinder, find the
total surface area of the figure.
c. Using the above, find the volume of the composite figure.
2. Consider the net of a figure made of cubes with edge 4 cm.
a. What is the least number of cubes used to make the solid?
b. What is the surface area of the surface?
c. What is the volume of the surface?
3. A( 1,2,4) and B(5,-2,8)
a. How far apart are points A and B?
b. If A is the center of a sphere and B is on the sphere, write the equation of the sphere.
c. The point (1 ,2, k) is on the sphere from part b. Find a possible value of k.
Answer Key
1.
a.)Edges:
AB, BC,
CD, DE,
DF, AF,
QR, RS,
ST, TU,
UV, VQ,
AV, BQ,
CR, DS,
ET, FU;
Faces:
ABCDEF,
QRSTUV,
CRSD,
DSTE,
ETUF,
FUVC,
ABQR;
Vertices: A,
B, C, D, E,
F, Q, R, S,
T, U, V
b.) Edges:
VZ, VY,
VX, VW,
WZ, XW,
XY, YZ;
Faces:
VZY,
VXY,
VWX,
VWZ,
WXYZ;
Vertices:
V, W, X,
Y, Z
c.) Edges:
TR, TS,
ST, JK,
JL, KL,
RL, SK,
TJ;
Faces:
RST, JKL,
TRLJ,
TSKJ,
RSKL;
Vertices:
J, K, L, R,
S, T
a.) Base
edges: PA,
AT, TN,
NE, EP,
GB, BC,
CD, DF,
FG
Lateral
edges: PG,
AB, TC,
ND, EF
b.) Base
edges: AB,
BC, CD,
DE, EF,
FG,GA
Lateral
edges: VA,
VB, VC,
VD, VE,
VF, VG
c.) Base
edges:
WX, XQ,
QM, MW,
NP, PY,
YZ, ZN
Lateral
edges:
MN, WZ,
XY, QP
Faces:
ATNEP,
BCDFG,
ABCT,
TCDN,
NDFE,
EFGP,
PGBA
Vertices:
A, B, C,
D, E, F,
G, N, P
QXYP,
MWZN
Vertices:
Q, P, M.
N, W, X,
Y, Z
5.
2.
3. 2a: V=10; E=15; F=7: V-E+F=2
2b: V=8; e=14; F=8: V-E+F=2
4.
a.)
b.)Edges:
c.)Edges:
Edges:
AB, BC,
MQ, MW,
AB, TC,
CD, DE,EG, WX, XQ,
ND, EF,
FG, GA,
NP, PY,
PG, AT,
AV, BV, CV, YZ, ZN,
TN, NE,
DV, EV, FV, MN, WZ,
EP, PA,
GV
XY, QP
BC, CD,
Faces:
Faces:
DF, FG,
ABCDEFG, QMWX,
GB
ABV, BCV,
NPYZ,
CDV, DEV,
EFV, GFV,
AGV
Vertices: A,
B, C, D, E,
F, G, V
6.
a.)Lateral
b.)Lateral
c.)Lateral
faces:
faces:
faces:
AVQB,
VWZ,
TJLF,
BQRC,
CZY,
TJKS,
CRSD,
VYX,
RLKS
DSTE,
VXW
Bases:
ETUF,
Bases:
TRS, JKL
FUVC
WXYZ
Bases:
ABCDEF,
QRSTUV
5a: V=12; E=18; F=8: V-E+F=2
5b: V=5; E=8; F=5: V-E+F=2
Surface
Solid
Surface
7.
8.
9.
10.
a.)Square
b.) Ellipse
c.)Circle
11.
a.)Hexagon
b.)Rectangle
12. Surface
13. Solid
14. Solid
15.
a.)Rectangle
b.)Pentagon
c.)Octagon
c.)Trapezoid
16.
a.)Circle
b.)Ellipse
c.)Parabola
17.
a.)Oblique
Square
pyramid
b.)Right
Triangular
Prism
c.)Right
Hexagonal
Prism
d.)Right
Cone
e.)Oblique
Cylinder
26. net
18.
27. 29.5
28. Net
19.
20.
a.)Oblique
Triangular
Prism
d.) Right
Cylinder
b.)Oblique
Cone
e.) Right
Square
Pyramid
c.) Oblique
Hexagonal
Prism
29. Net
21.
30. Net
22.
31. Net
23. net
32. 4√2
33. a
24. net
b
34. a
25. net
b
35. a
b
36. a
b
37.
LA=69.72 cm2
SA=265.72 cm2
38.
LA=192 u2
SA=275.14 u2
2
39. 232 cm
40.
a.)Nets will vary
b.)184 cm2
41.
a.)
b.)
c.)
LA=(51+17√5)m LA=945 LA=32
2
=89.01 m2
u2
2.14
m2
SA=(53+17√5)
m2=91.01 m2
SA=113
9.86 u2
SA=33
2.14
m2
2
42. Nets will vary; LA= 416 ft ; SA=488 ft2
43. LA=330 u2
SA=453.87 u2
44. 262.54 u2
45.
a.) LA=63 m2
b.) 650 ft2
2
SA=105.44 m
SA=707.24 ft2
46. SA=5616in2
47. 33 ft2
48. LA=252cm2
SA=350 cm2
49. LA=1319.47 cm2; used dh
50. 416.75 m2
51. 27.49 in2
52. 1017.9 ft2
53.
a.) LA=179.7 cm2
b.) LA=1130.97 m2
2
SA=3204.4 cm
SA=1639.91 m2
54. 2865 cm2
55. 375.48 mm2
56. 16.49 in2
57. SA=95 m2
58. L=2√10 mm2
LA=50.6 mm2
SA=66.6 mm2
59.
a.) l=5 u
b.) l=9.49 u
LA=80 u2
LA=278.9 u2
SA=144 u2
SA=495 u2
2
60. SA=40.66 ft (▲ are not congruent)
61. 628.6 in2
62. LA=3744 cm2; SA=9729.97 cm2
63.
a.) l=√61 u
b.) l=12.02 u
2
LA= 187.45 u
LA=479.39 u2
2
SA=331.45 u
SA=876.99 u2
64. 1654.45 in2
65. L=21.47 cm
66.
a.) 60 ft2
b.) 314.7 cm2
2
67. 831.39 m
68. 9.2 ft
69. 5 cm
70. 9.21 u
71.
b.) LA=90.48 u2
a.) LA=252 ft2
2
SA=140.74 u2
SA=396ft
72. 5.73 cm
73. 7.07 ft
74. 3 cm
75. 8000 mi
76. r=7.2 u
77. r=7.6 u
78. 314 yd2
79. 8.9"
80. 279,601 mi
81. 10.6 u
82. 5.2 u
83. 201.06 yd2
84. 2.86 in
85.
a.) 45238.9
m2
b)1809.56
cm2
c)53.79
mm2
86. 52 mm2
87. r=3.99 cm
88.
a.) 907.9 m2
b.) 615.75 cm2
89.
a.) 7 cm
42 cm
1847.26 cm2
90.
a.) 8100 m2 b.) 256 cm2 c.) 729/ mm2
91. r=1.67 cm
92.
a.) 615.75 m2
b.) 572.56 m2
93.
a.) 4.5 cm
b.) 27 cm
c.) 763.4 cm2
94. $164
95.
a.) 576 ft3
b.) 308.88 cm3
96.
a.) 130
b.) 2045.99
c.) 17 m3
m3
u3
97.
a.) 180 cm3
b.) 681.31 u3
98. 228 cm3
99. 25.5 in3
100. 231.34 cm3
101.
a.) 715.45 ft3
102. 332.55 u3
103. 157,685.96 in3
104. 31.4 ft3
105. 1.72 in3
106. h=2.4 in
107. 882 cm3
108. 625.8 m3
109. 1237 cm3
110. 2.95 in3
111.
a.) 1620m3
112. 850.36 mm3
113.
a.) 32 mm3
114. 18.75 ft3
115. 850 cm3
116. 1214.3 cm3
117.
a.) 54.49 m3
118. 4356 in3
119. 816 cm3
120.
a.) 157.7 ft3
b.) 450u3
b.) 110.85 u3
b.) 73.41 u3
b.) 37,699.11 m3
c.) 1989.68 cm3
121. 1539.38 m3
122. 2.9 ft
123. 3.11 cm3
124. 446.2 cm3
125. 2598.78 ft3
126. 2.82 ft
127. 198.91 cm3
128.
a)288,000 m3
129. 265.96 cm3
130.
a.) 2572.4 m3
131.
a.) 808.17 cm3
b.) 538.78 cm3
c.) 66⅔%
b)457.3 cm3
c)366.61/2 mm3
b.) 1436.75 cm3
132.
b.) 63.65 m3
a.)121,500m3
b.)682.6cm3
c.)3280.5/2mm3
133. 30.06 cm2
134.
a.) 1436.76 m3
b.) 1288.2 m3
135.
a.) 5176.56 cm3
b.) 3451.04 cm3
c.) 66⅔%
136.
a.) 2.99
b.) 2.26
137. Figure 1 and 2 because heights are
the same AND their cross sections
have equal area.
138.
a.) 26.18
b.) 4
139. Figure1, 2, and 3 all have the same
heights but only figure 2 and 3 have
equal area cross sections.
140.
a.) Yes; k=4 or 1/4
b.) No
141.
a.) 2 to 5
b.) 4 to 25
c.) 8 to 125
142.
a.) 4 to 3
b.) 16 to 9
c.) 64 to 27
143.
a.) 2 to 1
b.) 4 to 1
c.) 8 to 1
144.
a.) Yes
b.) No
k=2 or 1/2
145.
a.) 6 to 7
b.) 36 to 49
c.) 216 to 343
146.
a.) 5 to 2
b.) 25 to 4
c.) 125 to 8
147.
a.) 3 to 5
b.) 9 to 25
c.) 27 to 125
148. See graphs
149. 5.196
150. 7.55
151. 7.07
152. 9.8
153. 7
154. r=6; (2,0,4)
155. r=5; (-3,0,7)
156. r=7; (3,-4,5)
157. On
158. Ex: (2,-7,10)
159. See graphs
160. 8.66
161. 9.43
162. 7.07
163. 10.49
164. 3.74
165. r=8; (-3,0,-5)
166. r=2√5; (-6,0,8)
167. r=12; (5,-2,-10)
168. Outside
169. Ex: (5,0,4)
Multiple Choice
1. C
2. C
3. D
4. D
5. A
6. C
7. C
8. A
9. C
10. C
11. A
12. C
13. C
Extended Response
1. A. 8’ B. 192𝜋 𝑓𝑡 2 C. 384𝜋 𝑓𝑡 3
2. A. 6 cubes B. 416 cm2 C. 384 cm3
3. A. 6.9 u B. (x-1)2+(y-2)2+(z-4)2=48
C. 2.9 or 10.9