Happy

12/12/12!

• 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

Students will be able to solve for perimeter, area and volume by….

1. Finding the Perimeter & Area of Rectangles & Parallelograms

2. Finding the Perimeter and Area of Triangles and Trapezoids

3. Solving Right Triangles using the Pythagorean Theorem

4. Finding the Circumference and Area of Circles

5. Understanding How to Draw Three-Dimensional Figures

6. Finding the Volume of Prisms and Cylinders

7. Finding the Volume of Pyramids and Cones

8. Finding the Surface Area of Prisms and Cylinders

9. Finding the Surface Area of Pyramids and Cones

10. Finding the Volume and Surface Area of Spheres

Pre-Algebra

6-10 Spheres

Learning Goal Assignment

Learn to find the volume and surface area of spheres.

Pre-Algebra

6-10 Spheres

Pre-Algebra HOMEWORK

Page 326

#1-13

Show Work!

Pre-Algebra

6-10 Spheres

Vocabulary

sphere

hemisphere

great circle

Pre-Algebra

6-10 Spheres

Sphere Formula Animation

http://www.youtube.com/watch?v=xuPl_8o_j7k&NR=1&feature=endscreen

Hey Burgess- Prep for Full Screen!

Pre-Algebra

6-10 Spheres

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.

Pre-Algebra

6-10 Spheres

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.

Pre-Algebra

6-10 Spheres

Pre-Algebra

6-10 Spheres

Additional Example 1: Finding the Volume of a Sphere

Find the volume of a sphere with radius 9 cm, both in terms of and to the nearest tenth of a unit.

= 972 cm3 3,052.1 cm3

Volume of a sphere

Substitute 9 for r.

43

V = r3

= (9)343

Pre-Algebra

6-10 Spheres

Try This: Example 1

Find the volume of a sphere with radius 3 m, both in terms of and to the nearest tenth of a unit.

= 36 cm3 113.0 m3

Volume of a sphere

Substitute 3 for r.

43

V = r3

= (3)343

Pre-Algebra

6-10 Spheres

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!

Pre-Algebra

6-10 Spheres

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

50.3 units2

Pre-Algebra

6-10 Spheres

Additional Example 2: Finding Surface Area of a Sphere

Find the surface area, both in terms of and to the nearest tenth of a unit.

= 36 in2 113.0 in2

S = 4r2

= 4(32)

Surface area of a sphere

Substitute 3 for r.

Pre-Algebra

6-10 Spheres

Try This: Example 2

The moon has a radius of 1738 km. Find the surface area, both in terms of and to the nearest tenth.

= 12,082,576 km2 37,939,288.6 km2

S = 4r2

= 4(17382)

Surface area of a sphere

Substitute 1738 for r.1738 km

Pre-Algebra

6-10 Spheres

Lesson Quiz: Part 1

Find the volume of each sphere, both in terms of and to the nearest tenth. Use 3.14 for .

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 .

36m3, 113.0 m3

85.3ft3, 267.8 ft3

2.25 mi2, 7.1 mi2

1936 in2, 6079.0 in23. r = 22 in

4. d = 1.5 mi

Pre-Algebra

6-10 Spheres

5. A basketball has a circumference of 29 in. To the nearest cubic inch, what is its volume?

Lesson Quiz: Part 2

412 in3