1. Surface Area and Volume of Spheres
Section 4.9
Standard: MM2G4 ab
Essential Questions: How do I find the surface area and volume of spheres? How does changing the radius or diameter affect the surface area and volume?

2. Formula: Surface Area of a Sphere

3. Find the surface area of the sphere, given that the radius is 9 inches.

4. 2. Find the surface area of the sphere, given that the diameter is 10 inches.
d = 2r
10 = 2r
5 = r

5. S = 4(4)2 S = 64 C = 2r S ≈ 201.06 ft2 8 = 2r 4 = r
3. Find the surface area of the sphere, given that the circumference of the sphere is ft.
S = 4(4)2
S = 64
C = 2r
8 = 2r
4 = r
S ≈ ft2

6. Formula: Volume of a Sphere

7. 4. Find the volume of the sphere, given that the radius is 8 inches.
V ≈ in.3

8. 5. Find the volume of the sphere, given that the diameter is 10 inches.
d = 2r
10 = 2r
5 = r
V ≈ in.3

9. 6. Find the volume of the sphere, given that the circumference of the sphere is ft.
C = 2r
8 = 2r
4 = r
V ≈ ft3

10. 4 6 4:6 or 2:3 4 6 4 9 16 36 Complete the table. 2 3 2 : 3
Sphere 1
Sphere 2
Ratio of each for Sphere 1: Sphere 2
Radius 2 3
2 : 3
Diameter
Circumference
Area of Great Circle
Surface Area
Volume 4 6
4:6 or 2:3 4 6
4:6 or 2:3 4 9
4:9 or 4:9
16
36
16:36 or 4:9

11. Ratio of each for Sphere 1: Sphere 2
Complete the table.
Sphere 1
Sphere 2
Ratio of each for Sphere 1: Sphere 2
Radius a b
a : b
Diameter
Circumference
Area of Great Circle
Surface Area
Volume 2a 2b
a : b
2a
2b
a : b
 a2
 b2
a2 : b2
4a2
4b2
a2 : b2
a3 : b3

12. a : b a2 : b2 a3 : b3 Scale Factor _____________
Area Ratios _______________
Volume Ratios _______________
a2 : b2
a3 : b3

13. 7. Two spheres have diameters 24 and 36.
a. What is the ratio of the areas?
b. What is the ratio of the volumes?
Ratio of volumes:
Radii:
Ratio of radii:
24 and 36
24 : 36 or 2 : 3
Ratio of areas:
22 : 32 or 4 : 9
23 : 33 or 8 : 27

14. The second sphere is ¼ the size of the first.
8. A sphere has a radius of 6 meters. The radius of a second sphere is 3 meters. (a.) How does the surface area of the second sphere compare the to surface area of the first sphere? (b.) Volumes?
Ratio of radii:
3 : 6
or : 2
(a). Ratio of areas:
12 : 22
or : 4
The second sphere is ¼ the size of the first.
(The area of the second sphere is 4 times smaller)
(b). Ratio of volumes:
13 : 23
or : 8
The second sphere is 1/8 the size of the first.
(The volume of second sphere is 8 times smaller)

15. Ratio of surface areas: 12 : 22 or 1 : 4
9. The radius of a sphere is 2.4 cm. (a.) How will the surface area change if the radius is doubled? (b.) Volume?
Double the radius:
2(2.4) = 4.8
Ratio of radii:
2.4 : or 1 : 2
Ratio of surface areas:
12 : or 1 : 4
The surface area is 4 times larger if the radius is doubled.
Ratio of volumes:
13 : or 1 : 8
The volume is 8 times larger if the radius is doubled.

16. 10. Find the surface area of one hemisphere of
Find the surface area of one hemisphere of a circle if the circumference of a great circle of the sphere is 7 cm.
C = 2r
7 = 2r
7/2 = r
Surface area of entire
sphere: S = 4r2
S = 4 (3.5)2
S = 49
S ≈ cm2
Area of base
of hemisphere: A = r2
A =  (3.5)2
A = 12.25
A ≈ cm2
Surface area of hemisphere ≈ cm cm2
≈ cm2