1. Over Chapter 12 A.A B.B C.C D.D 5-Minute Check 2 32.0 cm 3 Find the volume of a cone with slant height of 4.3 centimeters and radius of 3.5 centimeters.

2. Over Chapter 12 A.A B.B C.C D.D 5-Minute Check 3 452.4 m 3 Find the volume of a hemisphere with radius of 6 meters.

3. Over Chapter 12 A.A B.B C.C D.D 5-Minute Check 5 131.9 yd 2 Find the surface area of a cone with slant height of 8.5 yards and radius of 3.5 yards.

4. Over Chapter 12 A.A B.B C.C D.D 5-Minute Check 6 18.0 in. The volume of a sphere is 24,429 cubic inches. What is the radius of the sphere?

5. Then/Now Represent sample spaces. Use the Fundamental Counting Principle to count outcomes.

6. Example 1 Represent a Sample Space One red token and one black token are placed in a bag. A token is drawn and the color is recorded. It is then returned to the bag and a second draw is made. Represent the sample space for this experiment by making an organized list a table, and a tree diagram. Organized List Pair each possible outcome from the first drawing with the possible outcomes from the second drawing. R, RB, B R, BB, R

7. Example 1 Represent a Sample Space Table List the outcomes of the first drawing in the left column and those of the second drawing in the top row.

8. Example 1 Represent a Sample Space Tree Diagram

9. A.A B.B C.C D.D Example 1 One yellow token and one blue token are placed in a bag. A token is drawn and the color is recorded. It is then returned to the bag and a second draw is made. Choose the correct display of this sample space. A.B. C.D.Y, Y; B, B; Y, B

10. Example 2 Multi-Stage Tree Diagrams CHEF’S SALAD A chef’s salad at a local restaurant comes with a choice of French, ranch, or blue cheese dressings and optional toppings of cheese, turkey, and eggs. Draw a tree diagram to represent the sample space for salad orders. The sample space is the result of 4 stages. ●Dressing (F, R, or BC) ●Cheese (C or NC) ●Turkey (T or NT) ●Eggs (E or NE) Draw a tree diagram with 4 stages.

11. Example 2 Multi-Stage Tree Diagrams Answer:

12. A.A B.B C.C D.D Example 2 5 BASEBALL GAME In the bleachers at a major league game you can purchase a hotdog, bratwurst, or tofu dog. This comes with the optional choices of ketchup, mustard, onions, and/or relish. How many stages are in the sample space?

13. Concept

14. Example 3 Use the Fundamental Counting Principle CARS New cars are available with a wide selection of options for the consumer. One option is chosen from each category shown. How many different cars could a consumer create in the chosen make and model? Use the Fundamental Counting Principle. exteriorinteriorseatenginecomputerwheelsdoorspossible colorcoloroutcomes 1175364383,160 ××××××= Answer:So, a consumer can create 83,160 different possible cars.

15. A.A B.B C.C D.D Example 3 3,888 BICYCLES New bicycles are available with a wide selection of options for the rider. One option is chosen from each category shown. How many different bicycles could a consumer create in the chosen model?

16. End of the Lesson