Happy 12/12/12!

1. Happy 12/12/12!

2. 12 Notable 12s • 12 months in a year • 12 hours on a clock face • 12 inches in a foot • 12 strikes to bowl to perfect game • 12 people have walked on the moon • 12 face cards in a deck • 12 days of Christmas (starting today) • 12 jurors in felony trials • 12 signs of the Zodiac • 12 pairs of ribs in most humans • 12 Greek Gods of Olympus • 12 items in a dozen

3. Students will be able to solve for perimeter, area and volume by…. • Finding the Perimeter & Area of Rectangles & Parallelograms • Finding the Perimeter and Area of Triangles and Trapezoids • Solving Right Triangles using the Pythagorean Theorem • Finding the Circumference and Area of Circles • Understanding How to Draw Three-Dimensional Figures • Finding the Volume of Prisms and Cylinders • Finding the Volume of Pyramids and Cones • Finding the Surface Area of Prisms and Cylinders • Finding the Surface Area of Pyramids and Cones • Finding the Volume and Surface Area of Spheres

4. Learning Goal Assignment Learn to find the volume and surface area of spheres.

5. Pre-Algebra HOMEWORK Page 326 #1-13 Show Work!

6. Vocabulary sphere hemisphere great circle

7. Sphere Formula Animation http://www.youtube.com/watch?v=xuPl_8o_j7k&NR=1&feature=endscreen Hey Burgess- Prep for Full Screen!

8. 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 hemisphereis agreat circle.

9. 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.

11. 4 3 V = pr3 = p(9)3 4 3 Additional Example 1: Finding the Volume of a Sphere Find the volume of a sphere with radius 9 cm, both in terms of p and to the nearest tenth of a unit. Volume of a sphere Substitute 9 for r. = 972p cm3 3,052.1 cm3

12. 4 3 V = pr3 = p(3)3 4 3 Try This: Example 1 Find the volume of a sphere with radius 3 m, both in terms of p and to the nearest tenth of a unit. Volume of a sphere Substitute 3 for r. = 36p cm3 113.0 m3

13. Surface Area of a Sphere http://www.youtube.com/watch?v=6YLH072aWP8 http://www.youtube.com/watch?v=RWbLzSMe_Uw Prep It Before You Present It!

14.  50.3 units2 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 of a unit. Surface area of a sphere S = 4pr2 = 4p(32) Substitute 3 for r. = 36p in2 113.0 in2

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

17. Lesson Quiz: Part 1 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, 267.8 ft3 36p m3, 113.0 m3 1936p in2, 6079.0 in2 3.r = 22 in 4.d = 1.5 mi 2.25p mi2, 7.1 mi2

18. Lesson Quiz: Part 2 5.A basketball has a circumference of 29 in. To the nearest cubic inch, what is its volume? 412 in3