Name
Name
L E S S O N
M A S T E R
9-9
B
©
Q u e s tio n s o n S P U R O b je c tiv e s
L E S S O N
M A S T E R
9 -9 B page 2
7. At the left is a map of Mexico and Central
America. Color it using exactly three colors.
Then label as many countries as you can.
U s e s Objective I: A p p ly th e F o u r- C o lo r T h eo r em to m a p s .
1. a. State the Four-Color Theorem.
Sample:
Suppose regions which share a border of some
length must have different colors. Then any
map of regions on a plane or sphere can be
colored so that only four colors are needed.
1976
b. In what year was the Four-Color Theorem proved?
Samples are
given.
In 2 and 3, color each map using as few colors
as possible.
2.
M e x ic o
B e liz e
3.
H o n d u ra s
N ic a r a g u a
G u a te m a la
E l S a lv a d o r
4. Draw a map with seven regions that
can be colored with only two colors.
Sample:
5. Draw a map with seven regions
that requires four colors to be
colored.
Panam a
C o s ta R ic a
Sample:
8. How is a Mercator-projection map made?
by projecting the surface of the earth
onto the lateral edge of a cylinder
6. At the right is a map of
some of the central states
in the United States.
Color it using the least
number of colors.
9. a. Name a property that is not preserved
on a Mercator-projection map.
distance, area
collinearity,
betweenness
b. Name a property that is preserved
on a Mercator-projection map.
10. Describe two problems with using a map of the
world that is made up of gores.
GEOMETRY © Scott, Foresman and Company
GEOMETRY © Scott, Foresman and Company
R e p r e s e n ta tio n s Objective K : In ter p r et m a p s o f th e w o r ld .
Sample: Different parts of a country may be
on different gores; the shape tears easily
and is not convenient to use.
14 5
©
Name
Name
10B-1
©
Q u e s tio n s o n S P U R O b je c tiv e s
1. What is the difference between the surface area and the
lateral area of a 3-dimensional figure?
10.
Surface area is the total area of all surfaces
of the figure, while lateral area is the total
area of only the lateral surfaces.
GEOMETRY © Scott, Foresman and Company
2. a box with length 12 in., width
7 in., and height 8 in.
304 in2
a.
472 in2
b.
3. a right cylinder with base radius
5 cm and height 8.5 cm
4. a right pentagonal prism with
base area 72 mm2, base perimeter
32 mm, and height 35 mm
1120 mm2
a.
1264 mm2
b.
5. a right cylinder with base
circumference 18π ft and
height 10 ft
6. a cube with edge 3 yd
7. a cube with edge e
4e 2 units2
a.
6e 2 units2
b.
b.
8.
36 yd2
54 yd2
a.
b.
right cylinder
20πx 2 ≈ 62.8x 2 units2
2
2
2
b. 28πx ≈ 88.0x units
a.
a.
b.
85π ø 267.0 cm2
135π ø 424.1 cm2
a.
b.
57π ≈ 179.1 in
75π ≈ 235.6 in2
2
630 ft2
738 ft2
a.
b.
U s e s Objective H : A p p ly fo r m u la s fo r la ter a l a n d s u r fa ce a r ea o f p r is m s a n d
cy lin d er s to r ea l s itu a tio n s .
12. A section of concrete sewer pipe is 4 ft in diameter
and 8 ft long. Find the lateral area of the pipe.
32π ≈ 100.5 ft2
13. A wooden toy box measures .75 m
by .6 m by .5 m. Find the surface area
of the toy box.
2.25 m 2
180π ≈ 565.5 ft2
342π ≈ 1074.4 ft2
5"
9'
6'
14. Refrigerated biscuit dough comes in a cylindrical can
with diameter 2.5 in. and height 8 in. The bases are
aluminum and the lateral face is cardboard.
a. How many square inches of aluminum
3.125π
are used?
12"
5x
11.
3''
2 1'
9.
4x
1 0 -1 B page 2
9.5''
S k ills Objective A : C a lcu la te la ter a l a r ea s a n d s u r fa ce a r ea s o f cy lin d er s a n d
p r is m s fr o m a p p r o p r ia te len g th s , a n d vice ver s a .
In 2–9, a figure is described. a. Give its lateral area.
b. Give its surface area.
b.
M A S T E R
In 10 and 11, a net for a 3-dimensional figure is
shown. a. Give the lateral area of the figure.
b. Give the surface area of the figure.
Vo c a b u la r y
a.
L E S S O N
b. How many square inches of cardboard
are used?
20"
right triangle prism
600 in2
15. Pipe organs often have large wooden pipes shaped like
long, narrow boxes without bases. One of the largest
organ pipes, in Liverpool Cathedral, England, is
about 36 ft long, 2 ft 9 in. wide, and 3 ft 2 in. deep.
Find its lateral area.
660 in2
14 7
©
≈ 9.8 in2
20π ≈ 62.8 in2
426 ft2
14 8
267
GEOMETRY © Scott, Foresman and Company
L E S S O N
M A S T E R
a.
14 6
Name
Name
©
Q u e s tio n s o n S P U R O b je c tiv e s
10-2
B
S k ills Objective B: Calculate lateral areas and surface areas of pyramids and
cones from appropriate, leng th s, and vice versa.
3. a regular square pyramid with
slant height of 5 in. and base area
of 49 in2
70 in2
a.
119
in2
b.
4. a right cone with circumference
of base 14π ft and slant height
of 8 ft
56π ≈ 175.9 ft2
a.
105π
≈ 329.9 ft2
b.
5. a regular square pyramid with
slant height of t and base edge
of u
2tu units2
a.
2
tu
1 u 2 units2
b.
6. a right cone with radius
j and slant height of 2j
7.
8.
a.
b.
a.
b.
8
6
e. What is the ratio of the surface area of the cone
to the surface area of the pyramid?
12. A paper weight is shaped like a regular square
pyramid with a base edge of 8 cm and a height
of 6.5 cm. Find its surface area.
Ï65 ≈ 405.3 un.
(16Ï65 1 64)π ≈
606.3 units2
a.16π
6
π
4
π
4
U s e s Objective H : A pply formulas for lateral and surface area of pyramids and
cones to real situations.
2
14 9
©
Name
≈ 186 cm2
13. A clown’s hat is in the shape of a right cone with a
radius 3.5 in. and a height 10 in. Find its lateral area.
≈ 116 in2
14. A watch crystal, shown at the right, is shaped
like the lateral sides of a regular pyramid
having a 12-sided base. If the slant height is
17 mm and the perimeter of the base is
96 mm, what is its lateral area?
816 mm2
15. Paper covers for ice-cream cones are made of
heavy paper. Cone A has a radius of 1 in. and
a slant height of 4 in. Cone B has a radius
of 1.25 in. and a slant height of 3.5 in.
Which cone contains more paper?
cone B
15 0
Name
L E S S O N
M A S T E R
©
Q u e s tio n s o n S P U R O b je c tiv e s
10-3
B
L E S S O N
1. A glass bottle is filled with sand.
a. Is the volume of the bottle better represented by
the amount of glass or the amount of sand?
b. Is the surface area of the bottle better represented
by the amount of glass or the amount of sand?
sand
glass
11. 512
528 cm3
________________
5. 11 mm, 11 mm, 11 mm
1331 mm3
________________
3. 2.4 in., 6 in., 6 in.
4.
86.4 in3
________________
8. Refer to the boxes at the right.
a. Find the surface area of
each box.
184 units2, 184 units2
13. 7000
15. 45
2
1
3
3 yd, 2 yd, 24 yd
11
yd3
7. 5 in., 5 ft, 5 yd
54,000 in3
________________
4
14
160 units , 112 units
3
3
c. Study your answers in Parts a and b.
What do you notice?
b. Find the volume of each box.
2
6
6
6
4.9
.5
4.6
16 m
72.2 ft2
19. A carton contains 16 ounces of cream. How many
cubic inches is this?
≈ 29 in3
20. Which holds more, a metal foot locker 26 in. by 14 in.
by 12 in., or a carton 22 in. by 16 in. by 13 in.?
carton
21. The inside dimensions of a freezer are 32 in. by
28 in. by 60 in. Find its volume in cubic feet.
≈ 31 ft3
b. Find the total volume of the 2 steps shown.
c. How many gallons of water would be displaced
if the steps shown were built totally submerged
into a pond?
9
12
216 units3, 216 units3
c. Study your answers in Parts a and b.
What do you notice?
Volumes are equal, but surface areas are not.
15 1
268
16. 100
22. The dimensions of each brick
at the right are 2 in., 3.5 in.,
and 8 in.
a. Find the volume of a
single brick.
56 in3
Surface areas are equal, but volumes are not.
9. Refer to the boxes at the right.
a. Find the surface area of
each box.
216 units2, 300 units2
14. 0.14887
8 units
U s e s Objective I: A pply formulas for volumes of rectang ular prisms to real
situations.
2
4
12. 117.649
18. The volume of a cube is about 614 ft3. What is
the area of a face, to the nearest tenth?
8
5
8
19.1
3.6
17. Find the length of the edge of a cube whose
volume is 4,096 m3.
12
________________
6. x, 2x, 3x
6x 3 units3
________________
b. Find the volume of each box.
1 0 -3 B page 2
S k ills Objective C: Calculate cube roots.
In 11–16, give the cube root of the number. Round inexact
answers to the nearest tenth.
S k ills Objective A : Calculate volumes of rectang ular prisms from appropriate
leng th s, and vice versa.
In 2–7, give the volume of the boxes with the
given dimensions.
2. 6 cm, 11 cm, 8 cm
M A S T E R
10. The volume of a box is 624 units3. Two of the
dimensions are 6 units and 13 units. Find the
third dimension.
V o c a b u la r y
GEOMETRY © Scott, Foresman and Company
8
c. What is the ratio of the lateral area of the cone
to the lateral area of the pyramid?
d. Find the surface area of each.
96π units2, 384 units 2
right cone
b.
14 mm
b. Find the lateral area of each.
60π units2, 240 units2
8
195 1 25Ï3 units2
216 units2
10. The slant height of a regular square pyramid is 20 mm
and its lateral area is 560 mm2. What is the length
of a base edge?
10 units, 10 units
14
regular triangular pyramid
slant height 13, base edge 10,
altitude of base 5Ï3
195 units2
9. Find the lateral area of a regular hexagonal pyramid
with a slant height of 9 and a base edge of 8.
a. Find the slant height of each.
2π j 2 ≈ 6.3j 2 units2
3π j 2 ≈ 9.4j 2 units2
10
1 0 -2B page 2
11. Pictured at the right are a right
cone and regular square pyramid.
13
5 3
M A S T E R
©
15 2
16,128 in3
≈ 70 gal.
GEOMETRY © Scott, Foresman and Company
GEOMETRY © Scott, Foresman and Company
In 1– 8, a figure is described. a. Give its lateral area.
b. Give its surface area.
1. a regular square pyramid with
2. a right cone with radius
slant height of 2 yd and base edge
6 cm and slant height of 9 cm
of 1 yd
2
4
yd
54π ≈ 169.6 cm2
a.
a.
5 yd2
90π ≈ 282.7 cm2
b.
b.
L E S S O N
UCSMP Geometry © Scott, Foresman and Company
L E S S O N
M A S T E R
Name
Name
10-4
B
L E S S O N M A S T E R 10- 4B page 2
©
Questions on SPUR Objectives
Properties Objective E: D etermine what happens to the surface area and
volume of a fi gure when its dimensions are multiplied
by some number(s).
Representations Objective J : R epresent products of two (or three) numbers
or expressions as areas of rectangles (or
volumes of boxes), and vice versa.
1. A box has a volume of 450 m3.
In 5–10, a diagram is shown. a. Write the
multiplication of polynomials represented by the
diagram. b. Find the product of the polynomials.
a. If one dimension of the box is doubled,
what is the volume of the larger box?
900 m
3
1800 m
c. If all three dimensions of the box are doubled,
what is the volume of the larger box?
3600 m
2
(m 1 r )(m 1 n)
2
b. m 1 mn 1 mr 1 nr
c. If one dimension of the box is multiplied by 5,
another dimension is doubled, and the third
dimension is tripled, what is the volume of the
larger box?
6000 ft
7.
4. A box has dimensions ,, w, and h. If the dimensions are
changed as indicated, give the volume of the new box.
x
b. Its length is multiplied by 3, its
width by 6, and its height by 10.
180 <wh
(< 1 5)(w 1 5)(h 1 5) or
<wh 1 5wh 1 5<h 15<w 1 25h 1 25w 1 25< 1 125
y
z
1
4
q
6
(r 1 4)(p 1 1)(q 1 6)
b. rpq 1 rq 1 4pq 1
4q 1 6rp 1 6r 1
24p 1 24
a.
©
Name
x
6
x
7
x11
12. a. Draw a diagram that models (x 1 2)(x 1 7).
2
b. Give the product. x 1 9x 1 14
c. Five is added to each dimension.
x
2
154
Name
LESSON
MASTER
10-5
B
©
Questions on SPUR Objectives
L E S S O N M A S T E R 10-5B page 2
Skills Objective A: Calculate volumes of cylinders and prisms from appropriate
length, and vice versa.
Properties Objective G : Know the conditions under which Cavalieri’s P rinciple
can be applied.
In 1–5, calculate the volume of the figure with the
specified dimensions.
11. Multiple choice. List all of the rectangular prisms
below that may be paired with the one at the right
under Cavalieri’s Principle.
1.
2.
8
3.
10
22
10
a, b
25
9
6
10
7
441π ≈
________________
1385.4 units3
4.
8
(a)
3025π ≈
________________
9503.3 units3
400 units3
________________
5.
(b)
3
circumference 25π mm
1250π ≈
________________
3927.0 mm3
(c)
12
4
4
8
5
14
8
Uses Objective I: Apply formulas for volumes of prisms and cylinders to real
situations.
II
12. In terms of volume, list the
cans at the right in order
from the smallest to largest.
20 m2
II ______
I
______
6 ft
8. What is the volume of a regular hexagonal prism
with a base area of 24Ï3 cm2 and a height of 12 cm?
288Ï3 cm3
10. A square prism and a cylinder have the same height
of 13 mm and the same volume of 832 mm3. Which
is greater, the base edge of the prism or the diameter
of the base of the cylinder?
6
12
12
7. What is the radius of a cylinder that has a volume of
108π ft3 and a height of 3 ft?
9. What is the length of a base edge of an oblique
square prism with a height of 42 in. and a volume
of 168 in3?
10
10
216 units3
________________
6. What is the area of the base of a prism that has a
volume of 140 m3 and a height of 7 m?
(d)
10
6
8mm
GEOMETRY © Scott, Foresman and Company
r
p
11. The sum of the areas of the four small
rectangles at the right is x2 1 7x 1 6.
If the length of the largest rectangle is
x 1 6, what is the width?
4 <wh
153
b.
10.
h
a. (f 1 g 1 h)(x 1 y 1 z)
b. fx 1 fy 1 fz 1 gx 1
gy 1 gz 1 hx 1
hy 1 hz
It is multiplied by
It is multiplied by k 3.
a. Just the length is multiplied by 4.
g
f
(a 1 b)(a 1 c 1 d )
a 2 1 ac 1 ad 1
ab 1 bc 1 bd
a.
14u 2 1 50u 1 24
b.
9.
b
c
d
(7u 1 4)(2u 1 6)
a.
3
1
8.
d. multiplied by k?
a
a
6
It is multiplied by 27.
It is multiplied by 125.
c. multiplied by 12?
8.
2u
3. What happens to the volume of a box if all
three dimensions are
b. multiplied by 5?
b.
4
7u
(x 1 4)(y 1 2)
xy 1 2x 1 4y 1 8
a.
III
5"
I
III
______
3.5"
6"
13. Find the volume of the flower tray at the
right. Its end pieces are shaped like
isosceles trapezoids.
2640 in3, or ≈ 1.5 ft3
2 in.
diameter
155
©
4"
2"
5"
1'
8"
10"
2.5'
14. How many gallons of oil can be stored in a
cylindric tank 8 feet long with a 5-foot
diameter? (1 cubic foot 5 7.5 gallons)
≈ 1178 gal.
15. Find the total weight of 30 steel rods shaped like
regular hexagonal prisms with 3-inch sides and
20 feet long. The density of steel is 490 pounds
per cubic foot.
≈ 47,740 lb
156
269
GEOMETRY © Scott, Foresman and Company
GEOMETRY © Scott, Foresman and Company
2000 ft3
y
a.
1000 ft3
b. If one dimension of the box is multiplied by 5
and another dimension is doubled, what is the
volume of the larger box?
4
x
6.
n
3
a. If one dimension of the box is multiplied
by 5, what is the volume of the larger box?
r
m
3
2. A box has a volume of 200 ft3.
a. tripled?
m
5.
b. If two dimensions of the box are doubled,
what is the volume of the larger box?
GEOMETRY © Scott, Foresman and Company
LESSON
MASTER
Name
Name
L E S S O N
M A S T E R
©
Q u e s tio n s o n S P U R O b je c tiv e s
10-6
B
L E S S O N
M A S T E R
6.
1 0-6 B page 2
7.
8.
P r o p e r tie s Objective F: Develop formulas for specific figures from more
gen eral formulas.
1. a. What is the special formula for the volume of a cylinder?
V 5 π r 2h
<
s
,
e
s
regular
pentagonal pyramid
b. Explain how the formula in Part a was derived from the
basic formula for the volume of a cylindric surface.
Substitute π r 2 for B in the formula
regular square
pyramid
L.A. 5 25 s<
V 5 Bh.
cube
L.A. 5 2s<
_________________
L.A. 5 4e 2
_________________
In 9–11, give a formula for each measure.
9.
2. a. What is the special formula for the surface area of a
right cone?
S.A. 5 π r< 1 π r 2
10.
k
1
Use S.A. 5 L.A. 1 B. For L.A., use 2<p and
d
m
surface area of
the right cone
lateral area of
right cylinder
S.A. 5
_________________
3π kp 1 π k 2
L.A.
5 4π m 2
_________________
volume of right
cylinder
V 5 π d 2h
4
5.
12.
r
13.
14.
18 ’
h
8
12
10 ’
12
h
h
5
s
right cylinder
regular
square pyramid
180π ft2
a. _____________
units2
a. 260
_____________
342π ft2
b. _____________
units2
b. 360
_____________
s
right cylinder
GEOMETRY © Scott, Foresman and Company
R e v ie w Objective A , L esson 10 - 1; Objective B , L esson 10 - 2
In 12–14, a figure is shown. a. Give its lateral area.
b. Give its surface area.
In 3–8, write a specific lateral-area formula for each figure.
regular triangular
prism
L.A.
5 2π rh
_________________
right square prism
L.A.
5 3sh
_________________
L.A. 5 4sh
_________________
15 7
©
Name
right cone
32Ï13π
units2
b. 32π (21
Ï13)units2
a.
15 8
Name
L E S S O N
M A S T E R
©
Q u e s tio n s o n S P U R O b je c tiv e s
10-7
B
In 1–9, find the volume of the figure.
1.
2.
9
34’
12
right cone
200 units3
_________________
324π ≈
_________________
U s e s Objective I: A pply formulas for volumes of py ramids an d con es to real
situation s.
9
26
14. Determine the volume of a cone-shaped coffee filter
that has a diameter of 4 in. and a height of 4 in.
cone with circumference
of base 36π
octagonal pyramid
with base area of 180
2808π ≈
_________________
8821.6 units3
540 units3
_________________
8.
21 mm
16. A wall pocket is a vase
that hangs on the wall.
Find the volume of one
that is half of a right
cone with diameter
17 cm and height
22 cm.
4''
4
16
2
7 mm
2''
12 mm
triangular pyramid
trapezoidal pyramid
294 mm3
_________________
216 units3
_________________
≈ 16.8 in3
9'
22'
21'
9.
18
16 π
3
15. Mr. Hong needs to calculate the volume of
his garage to determine which exhaust fan he
should buy. If the overall height of the
garage is 17 ft, find the volume, ignoring
wall and roof thicknesses.
5390 ft3
16
7.
x
3
6.
14
units3
x
1 to 3
1017.9 units3
right square pyramid
144Ï3 in2
rectangular pyramid
12,693 1 ft3
5.
512 Ï33
3
150 m
40 ’
triangular pyramid
4.
1 0-7B page 2
13. Pictured at the right is a square pyramid sitting on
a box. What is the ratio of the volume of the
pyramid to the volume of the box?
28’
15
8
M A S T E R
12. A hexagonal pyramid has a height of 15 in. and a
volume of 720Ï3 in 3. What is the area of the base?
3.
10
L E S S O N
11. A square pyramid has a base edge of 8.2 m and a
volume of 3362 m3. What is its height?
S k ills Objective B : C alculate volumes of py ramids an d con es from appropriate
len gths, an d vice versa.
UCSMP Geometry © Scott, Foresman and Company
2m
4
3π
right cone
≈ 4.2 in
17. What is the total
volume of the silo
pictured below?
18. Which of the
candles pictured
below contains
more wax?
3m
1''
3
6 m
I 13''
10. A cone has a volume of 504π cm3 and a height
of 14 cm. What is the diameter of its base?
12 cm
II
1''
3''
4m
3''
1''
≈ 832 cm3
________________
15 9
270
©
16 0
28
π ≈ 88 m3
________________
II
________________
GEOMETRY © Scott, Foresman and Company
GEOMETRY © Scott, Foresman and Company
substitute 2π r for p and simplify. For B,
substitute π r 2.
4.
11.
h
b. Explain how the formula in Part a was derived from
the basic formula for the lateral area of a right
conical surface.
3.
3p
Name
Name
LESSON
M A ST ER
©
Q u e s tio n s o n SP U R Ob je c tiv e s
10B- 8
In 7–10, give the radius of the sphere with the given
volume. Round inexact answers to the nearest tenth.
Sk ills Objective D : C a lcu la te th e vo lu m e o f a s p h ere fro m a p p ro p ria te len g th s ,
a n d vice vers a .
1. Refer to the sphere and the
cylinder containing two
cones shown at the right.
a. Inside the cylinder,
shade the space that
has the same volume
as the sphere.
7. 32
π cubic units
3
9. 52 ft3
r
r
6 in.
6.7 m
P r o p e r tie s Objective E : D eterm in e w h a t h a p p en s to th e vo lu m e o f a s p h ere
w h en its d im en s io n s a re m u ltip lied by s o m e n u m ber(s ).
11. Refer to the sphere at the right. What would
happen to its volume
a. if the radius
were doubled?
b. if the radius
were tripled?
two cones
It is multiplied by 8.
r
It is multiplied by 27.
is multiplied by 1000.
It is multiplied by 18 .
d. if the radius were halved?
3
.
e. if the radius were multiplied by k? It is multiplied by k
c. if the radius were multiplied by ten? It
In 2–4, draw the sphere with the given dimension.
Then find its volume.
3. radius 5 1.5 cm
10. 1262 m3
2.3 ft
2r
b. Complete the following. Given a cylinder with
radius r and height 2r containing two cones each
with radius r and height r, the volume of a sphere
with radius r is equal to the volume of ....?.... minus
the volume of ....?.....
2. radius 5 18 mm
8. 288π in3
2 units
r
the cylinder
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LESSON M A ST ER
4. diameter 5 1 in.
4.5π ≈ 14.1 cm
1π
6
≈ .5 in3
c. baseball, 23.5 cm in circumference
5. The radius of a sphere is 26 in.
a. Find the volume of the sphere to the nearest
cubic inch.
13. How many ounces of water are displaced if 120 glass
marbles are dropped into a 20-gallon aquarium, and
the diameter of each marble is 12 in.?
73,622 in3
b. Find the volume of the sphere to the nearest
tenth of a cubic foot.
42.6 ft3
6. The circumference of a great circle of a sphere
is 28π cm. What is its volume?
10,976 π
3
≈ 4.35 oz.
14. The diameter of an inflatable beach ball is 16 in. If
a person blowing it up exhales 120 cubic inches of
carbon dioxide with each breath, how many breaths
will it take to fill the ball?
≈
≈ 18 breaths
11,494 cm3
16 1
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Name
16 2
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LESSON
M A ST ER
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Q u e s tio n s o n SP U R Ob je c tiv e s
10B- 9
1. Refer to the sphere with great circle G
shown at the right. What is the ratio
of the surface area of the sphere to
the area of (G?
12. Refer to the sphere at the right. What would happen
to its surface area
a. if the radius
were doubled? It is multiplied by 4.
r
G
4 to 1
1 0 -9 B page 2
LESSON M A ST ER
P r o p e r tie s Objective E : D eterm in e w h a t h a p p en s to th e s u rfa ce a rea o f a
s p h ere w h en its d im en s io n s a re m u ltip lied by s o m e
n u m ber(s ).
Sk ills Objective D : C a lcu la te th e s u rfa ce a rea o f a s p h ere fro m a p p ro p ria te
len g th s , a n d vice vers a .
b. if the radius were tripled?
c. if the radius were multiplied by 10?
In 2–9, find the surface area of a sphere with the
given dimension.
2. radius 5 7
3. radius 5 18 mm
196π ≈ 615.8 units2
1296π ≈ 4071.5
4. diameter 5 38 cm
1444π ≈ 4536.5 cm
2
6. circumference of great
circle 5 16π ft
256π ≈ 804.2 ft2
UCSMP Geometry © Scott, Foresman and Company
≈ 137 cm3
≈ 29 cm3
≈ 219 cm3
b. table-tennis ball, 3.8 cm in diameter
GEOMETRY © Scott, Foresman and Company
7776π ≈
24,429.0 mm3
3
8. volume 5 972π cm3
324π ≈ 1017.9 cm2
d. if the radius were halved?
e. if the radius were multiplied by k?
mm2
5. diameter 5 5
25π ≈ 78.5 units
13. Estimate the surface area of each planet to the
nearest million square miles.
a. Venus, radius < 3750 miles
900π ≈ 2827.4 in2
b. Mars, radius < 2100 miles
c. Jupiter, radius < 44,500 miles
9. volume < 11,500 cubic units
≈ 2463 units2
11. The surface area of a sphere is 688 cm2. What
is its radius to the nearest tenth of a centimeter?
It is multiplied by 9.
It is multiplied by 100.
It is multiplied by 14 .
It is multiplied by k 2.
U s e s Objective I: A p p ly th e fo rm u la fo r th e s u rfa ce a rea o f a s p h ere to rea l
s itu a tio n s .
2
7. area of great circle < 225π in2
10. The radius of a sphere is 58 in.
a. Find the surface area of the sphere to the
nearest square inch.
b. Find the surface area of the sphere to the
nearest tenth of a square foot.
r
42,273 in2
293.6 ft2
177 million mi 2
55 million mi2
24,885 million mi2
14. The diameter of a plastic beach ball is 18 in. It is
made up of 12 gores, each a different color. How
many square inches of plastic are used for each gore?
≈ 85 in2
15. The United States launched its first communications
satellite, Echo I, in 1960. Find the area of the thin
metal that coated this 100-foot diameter balloon.
≈ 31,416 ft2
R e v ie w Objective C , E , a n d H , L es s o n s 2- 2 a n d 2- 3
In 16–19 a conditional statement is given. a. Tell if
the conditional is true. b. tell if its converse is true.
a 5 I am 16 years old today.
c 5 I am a teenager.
b 5 I cannot vote in the next year’s
d 5 I will be 17 in a year.
national election.
7.4 cm
16 3
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16. a ⇒ b
a.
18. c ⇒ a
a.
yes
no
b.
b.
no
yes
17. a ⇒ d
a.
19. b ⇒ c
a.
yes
no
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b.
b.
yes
no
GEOMETRY © Scott, Foresman and Company
GEOMETRY © Scott, Foresman and Company
U s e s Objective I: A p p ly th e fo rm u la fo r vo lu m e o f a s p h ere to rea l s itu a tio n s .
12. Find the volume of each ball.
a. tennis ball, 6.4 cm in diameter