Analytic Geometry A Accelerated Week 5    Page 37 of 46    Analytic Geometry A – Accelerated Week 5  Lesson 3.13     Volume of Prisms and Cylinders  Lesson 3.14     Volume of Pyramids and Cones  Lesson 3.15      Volume of Spheres  Lesson 4.1        Write Expressions in Radical and Exponential Form   Lesson 4.2        Extend the Properties of Exponents to Rational Exponents  Lesson 4.3        Use Properties of Rational and Irrational Numbers  Lesson 4.4      Simplify Complex Numbers   Lesson 4.5       Add and Subtract Complex Numbers  Lesson 4.6       Multiply Complex Numbers  Lesson 4.7       Divide Complex Numbers    Before working the problems, study the lesson listed above each problem set.  Record the answers on the answer sheet. Turn in the answer sheet to be  graded.     For some problem sets, answer boxes are given. Choices may be used more than  once if necessary.    Lesson 3.13     Volume of Prisms and Cylinders  Find the volume of the prisms.  1.        2.        3.  4.  Choices for 1‐4: (Answers are in cubic units.)  A) 42  B) 60  C) 118.8  D) 120  E) 237.6  AB) 420  AC) 720  AD) 726  AE) 864  BC) 1728  BD) 2400  BE) 2640          Analytic Geometry A Accelerated Week 5    Page 38 of 46    Find the indicated measure.  5. Find the height of a prism that has a volume of 96 cubic meters and the area of the base is 24  square meters.  6. A prism has a square base and a height of 5 in. The volume is 125 in 3 . Find the side length of  the square base.   7. A prism with a triangular base has a volume of 432 cubic feet. The height of the prism is 8  feet and the triangle base has a base of 12 feet. Find the height of the triangular base of the  prism.  Find the volume of the cylinders. Round to the nearest hundredths.  8.          9.          10.  Find the indicated measure. Round answer to nearest hundredths when necessary.  11. Find the height of a cylinder that has a volume of 1061.86 ft 3  and a radius of 6.5.  12. Find the radius of a cylinder that has a volume of 301.59 yd 3  and height of 6 yd.  13. Find the diameter of a cylinder that has a volume of 855.3 mm 3  and height of 6 mm.  Choices for 5‐7: (Answers are in appropriate units.)  A) 4  B) 4.5  C) 5  D) 6  E) 8  AB) 9  AC) 12  AD) 18   AE) 25   BC)  27  BD) 36   BE) 72   Choices for 11‐13: (Answers are in appropriate units.)  A) 4  B) 6  C) 8   D) 12   E) 16   AB) 6.74   AC) 8.38  AD) 13.47  AE) 25.13  BC) 32.64  BD) 42.51  BE) 45.38   Choices for 8‐10: (Answers are in cubic units.)  A) 62.83  B) 157.08  C) 314.16  D) 376.99  E) 942.48  AB) 1693.32  AC) 2261.95  AD) 2660.93  AE) 4561.59  BC) 4976.28  BD) 6773.27  BE) 16725.84          Analytic Geometry A Accelerated Week 5    Page 39 of 46    Lesson 3.14     Volume of Pyramids and Cones  Find the volume of the pyramid.  14.              15.  16.              17.  Find the indicated measure.   18. Find the area of the base of a pyramid that has .

1. Analytic Geometry A Accelerated Week 5 Page 37 of 46
Analytic Geometry A – Accelerated Week 5
Lesson 3.13 Volume of Prisms and Cylinders
Lesson 3.14 Volume of Pyramids and Cones
Lesson 3.15 Volume of Spheres
Lesson 4.1 Write Expressions in Radical and Exponential F
orm
Lesson 4.2 Extend the Properties of Exponents to Rational
Exponents
Lesson 4.3 Use Properties of Rational and Irrational Numb
ers
Lesson 4.4 Simplify Complex Numbers
Lesson 4.5 Add and Subtract Complex Numbers
Lesson 4.6 Multiply Complex Numbers
Lesson 4.7 Divide Complex Numbers
Before working the problems, study the lesson listed above each
problem set.
Record the answers on the answer sheet. Turn in the answer she

2. et to be
graded.
For some problem sets, answer boxes are given. Choices may be
used more than
once if necessary.
Lesson 3.13 Volume of Prisms and Cylinders
Find the volume of the prisms.
1. 2. 3.
4.
Choices for 1‐4: (Answers are in cubic units.)
A) 42 B) 60 C) 118.8 D) 120 E) 237.6 AB) 420
AC) 720 AD) 726 AE) 864 BC) 1728 BD) 2400 BE) 2640
Analytic Geometry A Accelerated Week 5 Page 38 of 46
Find the indicated measure.
5. Find the height of a prism that has a volume of 96 cubic mete
rs and the area of the base is 24

3. square meters.
6. A prism has a square base and a height of 5 in. The volume is
125 in
3
. Find the side length of
the square base.
7. A prism with a triangular base has a volume of 432 cubic feet
. The height of the prism is 8
feet and the triangle base has a base of 12 feet. Find the height
of the triangular base of the
prism.
Find the volume of the cylinders. Round to the nearest hundredt
hs.
8. 9. 10.
Find the indicated measure. Round answer to nearest hundredths
when necessary.

4. 11. Find the height of a cylinder that has a volume of 1061.86 ft
3
and a radius of 6.5.
12. Find the radius of a cylinder that has a volume of 301.59 yd
3
and height of 6 yd.
13. Find the diameter of a cylinder that has a volume of 855.3 m
m
3
and height of 6 mm.
Choices for 5‐7: (Answers are in appropriate units.)
A) 4 B) 4.5 C) 5 D) 6 E) 8 AB) 9
AC) 12 AD) 18 AE) 25 BC) 27 BD) 36 BE) 72
Choices for 11‐13: (Answers are in appropriate units.)
A) 4 B) 6 C) 8 D) 12 E) 16 AB) 6.74
AC) 8.38 AD) 13.47 AE) 25.13 BC) 32.64 BD) 42.51
BE) 45.38
Choices for 8‐10: (Answers are in cubic units.)
A) 62.83 B) 157.08 C) 314.16 D) 376.99 E) 942.48
AB) 1693.32
AC) 2261.95 AD) 2660.93 AE) 4561.59 BC) 4976.28
BD) 6773.27 BE) 16725.84

5. Analytic Geometry A Accelerated Week 5 Page 39 of 46
Lesson 3.14 Volume of Pyramids and Cones
Find the volume of the pyramid.
14. 15.
16. 17.
Find the indicated measure.
18. Find the area of the base of a pyramid that has a volume of
82 in
3
and a height of 12 in.
19. Find the height of a pyramid that has a square base with side
length 8 ft and a volume of

6. 192 ft
3
.
20. The volume of a pyramid that has a right triangular base wit
h legs that are 5 cm and 12 cm
long is 70 cm
3
. Find the height of the pyramid.
21. A pyramid has a volume of 120 yd
3
. The height of the pyramid is 9 yd. The base of the
pyramid is a rectangle that has a width of 8 yd. Find the length
of the rectangular base.
Choices for 14‐17: (Answers are in cubic units.)
A) 14 B) 25 C) 44 D) 45 E) 56 AB) 66
AC) 84 AD) 112 AE) 126 BC) 140 BD) 189 BE) 270
Choices for 18‐21: (Answers are in appropriate units.)
A) 3.5 B) 5 C) 6 D) 6.8 E) 7 AB) 9
AC) 12 AD) 15 AE) 20.5 BC) 24 BD) 27 BE) 36

7. Analytic Geometry A Accelerated Week 5 Page 40 of 46
Find the volume of the cone. Round to the nearest hundredth.
22. 23. 24.
Find the indicated measure. Round to nearest whole number.
25. Find the radius of a circular cone that has a volume of 339.2
9 m
3
and a height of 9 m.
26. Find the height of a circular cone that has a volume of 603.1
9 in
3
and a radius of 4 in.
27. Find the diameter of a circular cone that has a volume of 10
17.88 cm
3
and a height of 12
cm.
Lesson 3.15 Volume of Spheres

8. Find the volume of the sphere. Round to the nearest hundredth.
28. 29.
30. 31.
Choices for 22‐24: (Answers are in cubic units.)
A) 75.40 B) 138.23 C) 150.80 D) 172.79 E) 184.31
AB) 201.06
AC) 276.46 AD) 287.98 AE) 301.59 BC) 345.58 BD) 552.92
BE) 737.23
Choices for 25‐27: (Answers are in appropriate units.)
A) 6 B) 8 C) 9 D) 12 E) 15 AB) 16
AC) 18 AD) 21 AE) 23 BC) 24 BD) 36 BE) 72
Choices for 28‐31: (Answers are
in cubic units.)
A) 3.53 B) 4.19
C) 12.57 D) 14.14
E) 113.10 AB) 164.64

9. AC) 407.72 AD) 1317.09
AE) 1697.40 BC) 2144.66
BD) 3261.76 BE) 17157.28
Analytic Geometry A Accelerated Week 5 Page 41 of 46
Find the indicated measure. Round to nearest whole number.
32. Find the radius of a sphere that has a volume of 523.6 ft
3
.
33. Find the diameter of a sphere that has a volume of 113.1 m
3
.
Lesson 4.1 Write Expressions in Radical and Exponential For
m
Complete each property with the appropriate notation.
34.
1
2b 35.
1

10. nb 36.
m
nb
Choices for 34‐36
A) b B) nb
C) n b D) ( )nm b
E ) ( )mn b AB) 2b
Write each exponential expression in radical form.
37.
1
2619 38.
1
241 39.
1
315 40.
1
2(5 )x 41.
1
36x
42.
1

11. 2157 43.
1
42346 44.
2
3x 45.
3
4x
Choices for 37‐45
A)
2157 B) 315 C) 41 D) 157
E) 619 AB)
4
2346 AC) 3 15 AD) 4 2346
AE)
241 BC) 2619 BD) 5x BE) 3x
CD) 5 x CE) 3 2x DE) 3 4x ABC) 3 6x
ABD) 36 x ABE) 34 x
Choices for 32‐33: (Answers are in appropriate units.)
A) 3 B) 4 C) 5 D) 6 E) 7 AB) 8
AC) 9 AD) 10 AE) 12 BC) 14 BD) 16 BE) 18

12. Analytic Geometry A Accelerated Week 5 Page 42 of 46
Write each radical expression in exponential form.
46. 53 47. 7 x
48. 6x 49. 3 12
50. 4 x 51. 5 3xy
52. 6 5x 53. 3 25
Choices for 46‐53
A)
1
312 B)
1
253 C)
2
35 D)
2
312
E)
3
25 AB)
253 AC)

13. 1
5(3 )xy AD)
1
53( )xy
AE)
1
4x BC)
1
2(6 )x BD)
1
2(7 )x BE)
1
26x
CD)
1
27 x CE)
5
6x DE)
6
5x ABC)
4x
Simplify.

14. 54. 144 55. 3 216
56. 4 625 57. 5
243
58.
1
2100 59.
1
3343 60.
3
4625 61.
3
416
62.
4
327 63.
5
225 64.
10
38
Choices for 54‐64
A) 0 B) 1 C) 3 D) 5

15. E) 6 AB) 7 AC) 8 AD) 10
AE) 12 BC) 15 BD) 20 BE) 25
CD) 50 CE) 72 DE) 81 ABC) 111
ABD) 125 ABE) 1024 BCD) 3125
Analytic Geometry A Accelerated Week 5 Page 43 of 46
Lesson 4.2 Extend the Properties of Exponents to Rational Ex
ponents
Use the properties for rational exponents to simplify.
65.
2 13
66.
4
1 3
48
67.
1

16. --
327 68.
5
2
1
2
15
15
69.
1
--
264 70. 71.
42
7x
72.
015
16x

17. 73.
7
8
1
8
x
x
74.
9 11
4
Choices for 65‐74
A) B) C) 0 D)
1
8
E)
1
3
AB) 1 AC) 2 AD) 225

18. AE) 512 BC) 759, 375 BD)
3
168 BE)
26
58
CD)
5
1
x
CE)
2
7x DE)
3
4x ABC)
8
7x
ABD)
99
16x ABE)
ACD) 5x ACE) 7x
Lesson 4.3 Use Properties of Rational and Irrational Numbers

19. Identify as ‘A’ rational or ‘B’ irrational.
75. 121 76. 52 77.
0.85 78.
5
12
79. 80. 2536
Identify each sum or product as ‘A’ rational or ‘B’ irrational.
81. 82. 83.
3 6
5 11
84.
85. 86.
2
21
3
87. 88. 3 27
89.
Analytic Geometry A Accelerated Week 5 Page 44 of 46
Lesson 4.4 Simplify Complex Numbers

20. Write each complex number in standard form.
90. 91.
92.
93.
17
81
94.
95.
9
121
Choices for Problems 90‐95
A) 15i B) C) 2i D) 43i E)
3
11
i
AB) AC) 17i AD)
17
9
i
AE)

21. 17
9
i BC) 10i
BD) BE) 11i CD) CE) 43i DE)
9
11
i
Write each complex number in standard form.
96. 97.
98. 99.
Choices for Problems 96‐99
A) 9 B) C) 16 D) E) 2
AB) AC) 17 AD) AE)
BC)
BD) BE) 11 CD) CE)
DE)
ABC)

22. Analytic Geometry A Accelerated Week 5 Page 45 of 46
Lesson 4.5 Add and Subtract Complex Numbers
Add or subtract as indicated. C
hoices for problems 100‐108
100. 101.
102. 103.
104. 105.
106. (1 107.
108.
Lesson 4.6 Multiply Complex Numbers
Multiply. Write the answers in standard form. Choic
es for problems 109‐119
109. 2 (1

23. 110.
111.
112.
113.
114.
115.
116.
117.
118. (1 4
119.
A) AE)
B) 2 BC)
C) BD)
D) BE)
E) CD)
AB) CE)
AC) DE)

24. AD) ABC)
A) CD)
B) 26 CE)
C) DE)
D) ABC)
E) ABD)
AB) 20 ABE)
AC) ACD)
AD) ACE)
AE) ADE)
BC) BCD)
BD) BCE)
BE) CDE)
Analytic Geometry A Accelerated Week 5 Page 46 of 46
Lesson 4.7 Divide Complex Numbers
Find the complex conjugate. Ch
oices for problems 120‐125

25. 120.
121.
122. 3i
123.
124.
125.
Divide the complex numbers. Write the quotient as a complex n
umber in standard form.
Choices for problems 126‐130
126.
5
127.
2 4
6 3
i
i

26. 128.
2 9
7
i
i
129.
7 4
2 5
i
i
130.
4
6
i

27. i
A) AC) 3i
B) AD)
C) AE)
D) BC)
E) BD)
AB) BE) 8i
A)
21 7
10 10
AE)
8 2
15 3
B) BC)
2 43
7 21

28. C)
15 10
13 13
BD)
34 27
29 29
D)
9 2
7 7
BE)
2 13
3 16
E)
2 13
5 10
CD)
11 13
29 29
AB)

29. 21 7
8 8
CE) 0
AC)
9 2
7 7
DE)
2
3
i
AD)
1 2
6 3