1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Math Journal (5 Min)
K-W-L - Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write the “K” what they know and “W” what they want to know about the lesson before they have been taught the lesson, and at the end of class, write the “L” what they now know (Learned) about the lesson after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 sentence that they learned that pertained to the lesson.

3. Homework Review (5 Min)

4. Warm Up
1. Find the surface area of a square pyramid whose base is 3 m on a side and whose slant height is 5 m.
2. Find the surface area of a cone whose base has a radius of 10 in. and whose slant height is 14 in. Use 3.14 for .
39 m2
753.6 in2

5. Problem of the Day
Find the slant height of the cone with the following measurements:
The area of its base is one-third of its total surface area. The radius is 4 cm.
8 cm

6. Textbook Examples (I Do) (5 Min)

7. Learn to find the volume and surface area of spheres.

8. Vocabulary
sphere
hemisphere
great circle

9. A sphere is the set of points in three dimensions that are a fixed distance from a given point, the center. A plane that intersects a sphere through its center divides the two halves or hemispheres. The edge of a hemisphere is a great circle.

10. The volume of a hemisphere is exactly halfway between the volume of a cone and a cylinder with the same radius r and height equal to r.

12. Additional Example 1: Finding the Volume of a Sphere
Find the volume of a sphere with radius 12 cm, both in terms of p and to the nearest tenth. Use 3.14 for p. 4 3
V = pr3
Volume of a sphere
= p(12)3 4 3
Substitute 12 for r.
= 2304p cm3  7,234.6 cm3

13. 4 V = pr3 3 Volume of a sphere 4 = p(3)3 3 Substitute 3 for r.
Check It Out: Example 1
Find the volume of a sphere with radius 3 m, both in terms of p and to the nearest tenth. Use 3.14 for p. 4 3
V = pr3
Volume of a sphere
= p(3)3 4 3
Substitute 3 for r.
= 36p m3  m3

14. The surface area of a sphere is four times the area of a great circle.

15. Additional Example 2: Finding Surface Area of a Sphere
Find the surface area, both in terms of p and to the nearest tenth. Use 3.14 for p.
S = 4pr2
Surface area of a sphere
= 4p(32)
Substitute 3 for r.
= 36p in2  in2

16. Check It Out: Example 2
The moon has a radius of 1738 km. Find the surface area, both in terms of p and to the nearest tenth. Use 3.14 for p.
S = 4pr2
Surface area of a sphere
= 4p(17382)
Substitute 1738 for r.
1738 km
= 12,082,576p km2
 37,939,288.6 km2

17. Additional Example 3: Comparing Volumes and Surface Areas
Compare the volumes and surface areas of a sphere with radius 42 cm with that of a rectangular prism measuring 44 cm by 84 cm by 84 cm.
Sphere:
Rectangular Prism:
V = pr3= p(423) 4 3
V = lwh
 ,088 22 7 4 3
= (44)(84)(84)
 310,464 cm3
= 310,464 cm3

18. Additional Example 3 Continued
Sphere:
Rectangular Prism:
S = 4pr2 = 4p(422)
S = 2lw + 2lh + 2wh
S = 2(44)(84) + 2(44)(84)
+ 2(84)(84)
= 7,056p
 7,  22,176 cm2 22 7
= 28,896 cm2
The sphere and the prism have approximately the same volume, but the prism has a larger surface area.

19. Check It Out: Example 3
Compare the volume and surface area of a sphere with radius 21 mm with that of a rectangular prism measuring 22 by 42 by 42 mm.
Sphere:
Rectangular Prism:
V = pr3= p(213) 4 3
V = lwh  22 7 4 3
= (22)(42)(42)
 38,808 mm3
= 38,808 mm3

20. Check It Out: Example 3 Continued
Sphere:
Rectangular Prism:
S = 4pr2 = 4p(212)
S = 2lw + 2lh + 2wh
= 1764p
S = 2(22)(42) + 2(22)(42)
+ 2(42)(42)
  5544 mm2 22 7
= 7224 mm2
The sphere and the prism have approximately the same volume, but the prism has a larger surface area.

21. Class work Problems (We Do) (10 Min)
Pg (1-9)

24. Small Group CW(Yall Do) (10 Min)
Pg (10-26 EOE)

30. Homework (You Do) (10 Min)
Pg (11, 15, 19, 21, 23 odd)

31. Math Journal (5 Min)
K-W-L - Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write the “K” what they know and “W” what they want to know about the lesson before they have been taught the lesson, and at the end of class, write the “L” what they now know (Learned) about the lesson after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 sentence that they learned that pertained to the lesson.

32. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 32

33. Lesson Quiz: Part I
Find the volume of each sphere, both in terms of  and to the nearest tenth. Use 3.14 for p.
1. r = 4 ft
2. d = 6 m
Find the surface area of each sphere, both in terms of  and to the nearest tenth. Use 3.14 for p.
85.3p ft3, ft3
36p m3, m3
3. r = 22 in
1936p in2, in2
4. d = 1.5 mi
2.25p mi2, 7.1 mi2

34. Lesson Quiz: Part II
5. A basketball has a circumference of 29 in. To the nearest cubic inch, what is its volume?
412 in3

35. Lesson Quiz for Student Response Systems
1. Find the volume of a sphere with radius 5 ft, both in terms of p and to the nearest tenth. Use 3.14 for p.
A p ft3, ft3
B p ft3, ft3
C p ft3, ft3
D p ft3, ft3 35

36. Lesson Quiz for Student Response Systems
2. Find the volume of a sphere with a diameter of 8 m, both in terms of p and to the nearest tenth. Use 3.14 for p.
A p m3, m3
B p m3, m3
C. 85.3p m3, m3
D. 85.3p m3, m3 36

37. Lesson Quiz for Student Response Systems
3. A decorative lamp in the form of a sphere has a circumference of 32 inches. To the nearest cubic inch, what is its volume?
A. 554 in3
B. 562 in3
C. 571 in3
D. 580 in3 37