Name ________________________________________ Date __________________ Class__________________
LESSON
11-4
Reteach
Spheres
Volume and Surface Area of a Sphere
Volume
The volume of a sphere with radius r is
V
Surface Area
4 3
Sr .
3
The surface area of a sphere with radius r is
S
4Sr2.
Find each measurement. Give your answer in terms of S.
1. the volume of the sphere
2. the volume of the sphere
_________________________________________
________________________________________
3. the volume of the hemisphere
4. the radius of a sphere with volume
7776S in3
_________________________________________
________________________________________
5. the surface area of the sphere
6. the surface area of the sphere
_________________________________________
________________________________________
© Houghton Mifflin Harcourt Publishing Company
324
Holt McDougal Analytic Geometry
Name ________________________________________ Date __________________ Class__________________
LESSON
11-4
Reteach
Spheres continued
The radius of the sphere is multiplied by
1
.
4
Describe the effect on the surface area.
new surface area, radius multiplied by
original surface area:
S
4Sr 2
4S(16)2
S
r
16
1024S m2 Simplify
Notice that 1024 x
1
16
1
:
4
4Sr 2
4S(4)2
r
64S m2
Simplify.
4
64. If the dimensions are multiplied by
1
,
4
2
1
§ 1·
.
the surface area is multiplied by ¨ ¸ , or
16
©4¹
Describe the effect of each change on the given measurement
of the figure.
7. surface area
8. volume
The radius is multiplied by 4.
The dimensions are multiplied by
_________________________________________
1
.
2
________________________________________
Find the surface area and volume of each composite figure.
Round to the nearest tenth.
9. Hint: To find the surface area, add the
lateral area of the cylinder, the area of
one base, and the surface area of the
hemisphere.
10. Hint: To find the volume, subtract the
volume of the hemisphere from
the volume of the cylinder.
_________________________________________
________________________________________
© Houghton Mifflin Harcourt Publishing Company
325
Holt McDougal Analytic Geometry
12. Consider the octahedron as two square
pyramids with different altitudes, h1 and
1
B(h1 h2) Note that altitude is
h 2. V
3
always a positive number.
9. The volume is multiplied by
10. S | 271.6 in2; V | 234.8 in3
11. S | 446.0 cm2; V | 829.4 cm3
Practice C
13. V | 433.3 units3
1. Possible answer:
Problem Solving
1. V | 940.0 m3
2. V
50.75S cm3
3. V | 210.8 cm3
4. V
98S in3
5. A
6. G
2. Possible answer: S
7. A
1. V | 3141.6 cm
3
2. V
3. V | 277.3 in3
28 ft
3. S
3
Practice A
1. V
4 3
Sr
3
2. S
4Sr2
3. V
288S cm3
4. V
486S in3
30 mm
256S ft2
9. V
36S m3; S
3
10. V 972S m ; S
8. S
64S yd2
36S m2
2
324S m
2. V
8. V
375S 3
in
32
4
S(x2 y2 z2)3
3
125S 3
9. V
in
32
1. V
500 S
mm3
3
2. V
3. V
16 S 3
ft
3
4. r
5. S
196S in2
6. S
2048 S
cm3
3
18 in.
400S m2
1
.
8
9. S | 1442.0 cm2; V | 4580.4 cm3
10. S | 216.8 in2; V | 141.4 in3
Challenge
3. d
5. S
4S(x2 y2 z2); V
8. The volume is multiplied by
3888S mm3
1
8788S 3
ft 2929 ft3
3
3
10m
250 S
4. V
cm3; V
3
7. S
6 in.
7. The surface area is multiplied by 16.
69S mi2
Practice B
1. V
6. h
Reteach
11. The volume is multiplied by 27. The
surface area is multiplied by 9.
81S mi3; S
4. h | 11.1 in.
2
10. 66 3
6. the sphere
7. S
3Sr2 Sr2
5. h | 6.9 in.
4. V | 3534.3 ft3
11-4 SPHERES
12. V
4Sr2 r2 r2 4 S 2 1
Reading Strategies
5. r
8
.
125
32 S
cm3
9
1. 16S in2; 24S in2; 16S in3; 16S in2;
32
S in3
3
2. 100S cm2; 150S cm2; 250S cm3; 100S
500
cm2;
S cm3
3
484S in2
48S yd2; S 16S yd2
1372 S
1
7. V
km3 457 S km3
3
3
8. The surface area is divided by 16.
6. S
3. 400S ft2; 600S ft2; 2000S ft3; 400S ft2;
4000
S ft3
3
© Houghton Mifflin Harcourt Publishing Company
A61
Holt McDougal Analytic Geometry