Spheres

1. Section 11-4
Spheres

2. Essential Questions
How do you find surface areas of spheres?
How do you find volumes of spheres?

3. Vocabulary
1. Great Circle:
2. Pole:
3. Hemisphere:

4. Vocabulary
1. Great Circle:
2. Pole:
3. Hemisphere:
A circle formed when a plane
intersects a sphere and the circle has the
same center as the sphere

5. Vocabulary
1. Great Circle:
2. Pole:
3. Hemisphere:
A circle formed when a plane
intersects a sphere and the circle has the
same center as the sphere
The endpoints of the diameter of a great
circle

6. Vocabulary
1. Great Circle:
2. Pole:
3. Hemisphere:
A circle formed when a plane
intersects a sphere and the circle has the
same center as the sphere
The endpoints of the diameter of a great
circle
One of the two congruent halves
of a sphere created by a great circle

7. Formulas
Surface Area of a Sphere:
Volume of a Sphere:

8. Formulas
Surface Area of a Sphere: SA = 4πr2
Volume of a Sphere:

9. Formulas
Surface Area of a Sphere: SA = 4πr2
Volume of a Sphere: V =
4
3
πr3

10. Example 1
Find the surface area of the sphere.

11. Example 1
Find the surface area of the sphere.
SA = 4πr2

12. Example 1
Find the surface area of the sphere.
SA = 4πr2
SA = 4π(4.5)2

13. Example 1
Find the surface area of the sphere.
SA = 4πr2
SA = 4π(4.5)2
SA ≈ 254.47 in2

14. Example 2
Find the surface area of a hemisphere with a
diameter of 8 mm to the nearest hundredth.

15. Example 2
Find the surface area of a hemisphere with a
diameter of 8 mm to the nearest hundredth.
SA = 1
2
i 4πr2
+ πr2

16. Example 2
Find the surface area of a hemisphere with a
diameter of 8 mm to the nearest hundredth.
SA = 1
2
i 4πr2
+ πr2
r = 1
2
d

17. Example 2
Find the surface area of a hemisphere with a
diameter of 8 mm to the nearest hundredth.
SA = 1
2
i 4πr2
+ πr2
r = 1
2
d
r = 1
2
(8)

18. Example 2
Find the surface area of a hemisphere with a
diameter of 8 mm to the nearest hundredth.
SA = 1
2
i 4πr2
+ πr2
r = 1
2
d
r = 1
2
(8)
r = 4 mm

19. Example 2
Find the surface area of a hemisphere with a
diameter of 8 mm to the nearest hundredth.
SA = 1
2
i 4πr2
+ πr2
r = 1
2
d
r = 1
2
(8)
r = 4 mm
SA = 2π(4)2
+ π(4)2

20. Example 2
Find the surface area of a hemisphere with a
diameter of 8 mm to the nearest hundredth.
SA = 1
2
i 4πr2
+ πr2
r = 1
2
d
r = 1
2
(8)
r = 4 mm
SA = 2π(4)2
+ π(4)2
SA ≈ 150.8 mm2

21. Example 3
Find the surface area of a sphere if the
circumference of the great circle is 14π inches.

22. Example 3
Find the surface area of a sphere if the
circumference of the great circle is 14π inches.
SA = 4πr2

23. Example 3
Find the surface area of a sphere if the
circumference of the great circle is 14π inches.
SA = 4πr2
C = 2πr

24. Example 3
Find the surface area of a sphere if the
circumference of the great circle is 14π inches.
SA = 4πr2
C = 2πr
14π = 2πr

25. Example 3
Find the surface area of a sphere if the
circumference of the great circle is 14π inches.
SA = 4πr2
C = 2πr
14π = 2πr
2π 2π

26. Example 3
Find the surface area of a sphere if the
circumference of the great circle is 14π inches.
SA = 4πr2
C = 2πr
14π = 2πr
2π 2π
r = 7 in.

27. Example 3
Find the surface area of a sphere if the
circumference of the great circle is 14π inches.
SA = 4πr2
C = 2πr
14π = 2πr
2π 2π
r = 7 in.
SA = 4π(7)2

28. Example 3
Find the surface area of a sphere if the
circumference of the great circle is 14π inches.
SA = 4πr2
C = 2πr
14π = 2πr
2π 2π
r = 7 in.
SA = 4π(7)2
SA ≈ 615.75 in2

29. Example 4
Find the volume of the sphere rounded to the
nearest hundredth.

30. Example 4
Find the volume of the sphere rounded to the
nearest hundredth.
V =
4
3
πr3

31. Example 4
Find the volume of the sphere rounded to the
nearest hundredth.
V =
4
3
πr3
V =
4
3
π(4.5)3

32. Example 4
Find the volume of the sphere rounded to the
nearest hundredth.
V =
4
3
πr3
V =
4
3
π(4.5)3
V ≈ 381.70 in3

33. Example 5
Find the volume of a hemisphere with a diameter
of 6 feet to the nearest hundredth.

34. Example 5
Find the volume of a hemisphere with a diameter
of 6 feet to the nearest hundredth.
V =
1
2
i
4
3
πr3

35. Example 5
Find the volume of a hemisphere with a diameter
of 6 feet to the nearest hundredth.
V =
1
2
i
4
3
πr3 r = 1
2
d

36. Example 5
Find the volume of a hemisphere with a diameter
of 6 feet to the nearest hundredth.
V =
1
2
i
4
3
πr3 r = 1
2
d
r = 1
2
(6)

37. Example 5
Find the volume of a hemisphere with a diameter
of 6 feet to the nearest hundredth.
V =
1
2
i
4
3
πr3 r = 1
2
d
r = 1
2
(6)
r = 3 ft

38. Example 5
Find the volume of a hemisphere with a diameter
of 6 feet to the nearest hundredth.
V =
1
2
i
4
3
πr3 r = 1
2
d
r = 1
2
(6)
r = 3 ft
V =
2
3
π(3)3

39. Example 5
Find the volume of a hemisphere with a diameter
of 6 feet to the nearest hundredth.
V =
1
2
i
4
3
πr3 r = 1
2
d
r = 1
2
(6)
r = 3 ft
V =
2
3
π(3)3
V ≈ 56.55 ft3

40. Example 6
Find the volume of a sphere that has a great
circle with an area of 9π square feet.

41. Example 6
Find the volume of a sphere that has a great
circle with an area of 9π square feet.
V =
4
3
πr3

42. Example 6
Find the volume of a sphere that has a great
circle with an area of 9π square feet.
V =
4
3
πr3
A = πr2

43. Example 6
Find the volume of a sphere that has a great
circle with an area of 9π square feet.
V =
4
3
πr3
A = πr2
9π = πr2

44. Example 6
Find the volume of a sphere that has a great
circle with an area of 9π square feet.
V =
4
3
πr3
A = πr2
9π = πr2
π π

45. Example 6
Find the volume of a sphere that has a great
circle with an area of 9π square feet.
V =
4
3
πr3
A = πr2
9π = πr2
π π
9 = r2

46. Example 6
Find the volume of a sphere that has a great
circle with an area of 9π square feet.
V =
4
3
πr3
A = πr2
9π = πr2
π π
r = 3 ft.
9 = r2

47. Example 6
Find the volume of a sphere that has a great
circle with an area of 9π square feet.
V =
4
3
πr3
A = πr2
9π = πr2
π π
r = 3 ft.
9 = r2
V =
4
3
π(3)3

48. Example 6
Find the volume of a sphere that has a great
circle with an area of 9π square feet.
V =
4
3
πr3
A = πr2
9π = πr2
π π
r = 3 ft.
9 = r2
V =
4
3
π(3)3
V ≈ 113.10 ft3

49. Problem Set

50. Problem Set
p. 822 #1-9 all
“With self-discipline most anything is possible.”
- Theodore Roosevelt