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COMMON CORE STATE STANDARDS:

8.G.9 – Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

STANDARDS FOR MATHEMATICAL PRACTICE:

2. Reason abstractly and quantitatively.6. Attend to precision. 7. Look for and make use of structure.

ENGAGE

Access students’ knowledge by asking the following questions:What do you know about finding volume?What information have you learned that could be applied to finding the volume of a cone, cylinder or sphere?What interests you about finding the volume of a cone, sphere, or cylinder?

EXPLORE

Explore students’ understanding and/or inquiry by asking:How do circles apply to finding the volume of a cone, cylinder, and/or sphere?What would you expect to happen to the volume of a cylinder if you double the height?What would you expect to happen to the volume of a cylinder if you double the radius?What would you expect to happen to the volume of a cone if you double the radius?What would you expect to happen to the volume of a cone if you double the height?What would you expect to happen to the volume of a sphere if you double the radius?

EXPLAIN

Have students explain their thoughts/ideas to the following questions:Explain how you might derive the formulas for finding the volume of a cone, cylinder and sphere.Explain how finding the volume of a cylinder is related to finding the area of a circle.Explain why we need a factor of ⅓ when computing the volume of a cone.

EXTEND

Extend student understanding by asking the following questions:Why do you think a cone is used for ice cream rather than a rectangular box?How do you think the volume of these objects applies to items you would see in a supermarket? How do these objects relate to marketing diSerent products?

Snow Cones, Sporting Equipment and Containers: Objectives

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94 The Casio Education Workbook Series: fx-300ES PLUS Book For the Middle Grades

Snow Cones, Sporting Equipment and Containers: Getting Started

Getting StartedIt’s time for your local county’s fair and time to enjoy a great snow cone. You are trying to determine which snow cone is the best deal for the price between a small, medium and large snow cone. Express answers in terms of and when appropriate, round answers to the nearest hundredth. (To simplify things, we will only deal with the cone; for a greater challenge, try figuring out the volume including the hemisphere of ice on top!)

1. What is the volume of the small snow cone?

2. What is the volume of the medium snow cone?

3. What is the volume of the large snow cone?

4. Which snow cone is the better deal and why? Explain your reasoning.

5. What happened to the volume of the snow cones when the radius doubled?

6. What happened to the volume of the snow cones when the radius tripled?

7. What happened to the volume of the snow cones when the height doubled?

8. What happened to the volume of the snow cones when the height tripled?

r = 2 in

h = 6 in

r = 4 in

h = 9 in

r = 6 in

h = 12 in

Small$1.00

Medium$1.50

Large$2.00

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? ?Snow Cones, Sporting Equipment and Containers: ProblemsProblems

1. Find the volume of a cylinder that measures 20 cm tall and has a radius of 5 cm.

a. What happens to the volume of the cylinder if you double the radius?b. What happens to the volume of the cylinder if you double the height?c. What happens to the volume of the cylinder if you double the height and double

the radius?

2. Find the volume of a sphere if the radius measures 7 in.

a. What happens to the volume of the sphere if you double the radius?b. What happens to the volume of the sphere if you triple the radius?

3. Find the volume of a cone that has a radius of 3 ½ inches and a height of 8 ¼ inches.

5 cm

20 cm

7 in

8.25 in

3.5 in

96 The Casio Education Workbook Series: fx-300ES PLUS Book For the Middle Grades

?Snow Cones, Sporting Equipment and Containers: Problems

4. Determine the volumes of the following sporting equipment.a. NBA Basketball with a radius of 9.3 inchesb. MLS Soccer Ball with a diameter of 28 inchesc. Regulation Volleyball with a radius of 8 inchesd. Bowling Ball with a diameter of 8.5 inchese. Golf Ball with a diameter of 1.68 inchesf. MLB Baseball with a radius of 1.5 inches

5. Physical therapists use medicine balls to help rehabilitate their patients.

Medicine Ball Radius Weight

A 5 inches 6 pounds

B 5 inches 10 pounds

C 9.5 inches 10 pounds

D 8.5 inches 8 pounds

E 7.5 inches 4 pounds

Determine the volume of each medicine ball and determine if there is any

correlation between the volume of the medicine ball and its weight. Explain your reasoning.

6. Storage containers shaped liked cylinders are used to hold diSerent dry goods in your kitchen. Determine the dimensions of various cylinders used to hold certain products.

a. A spice container with a volume between 50 in3 and 75 in3

b. A pasta container with a volume between 170 in3 and 200 in3

c. A cereal container with a volume between 435 in3 and 460 in3

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? Snow Cones, Sporting Equipment and Containers: AnswersGetting Started

1. 8 , 25.13 in3

2. 48 , 150.8 in3

3. 144 , 452.39 in3

4. Large $0.004 per cubic in

Medium $0.01 per cubic in

Small $0.04 per cubic in

The large snow cone is the better deal because it is the cheapest per cubic in

5. When the radius is doubled, the volume of the snow cone is 22 = 4 times as large.6. When the radius is tripled, the volume of the snow cone is 32 = 9 times as large.7. When the height is doubled, the volume of the snow cone is twice as large.8. When the height is tripled, the volume of the snow cone is 3 times as large.

, 150.8 in

144 , 452.39 in

deal because it is the cheapest per

98 The Casio Education Workbook Series: fx-300ES PLUS Book For the Middle Grades

Problems:1. Volume of cylinder is (5)2 = 500 1,570.8 cm3

a. Volume is 22 = 4 times larger.b. Volume is 2 times larger.c. Volume is 4 x 2 = 8 times larger.

2. Volume of a sphere is 43 (7)3 = 13723 1,436.76 in3

a. Volume is 23 = 8 times as large.b. Volume is 33 = 27 times as large.

3. Volume of a cone is ⅓ (3.5)2 (8.25) = 532

16 105.83 in3

4. Sports Equipment

a. NBA Basketball = 43 (9.3)3 3,369.28 in3

b. MLS Soccer Ball = 43 (14)3 = 10,976

3 11,494.04 in3

c. Regulation Volleyball = 2,0483 2,144.66 in3

Snow Cones, Sporting Equipment and Containers: Problems

olume of cylinder is (5)

ph 43 (7)

2 048Regula on olleybal 3

(3 ) (8

1,570.8 cm

3 ,4

3,369.28 in

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Snow Cones, Sporting Equipment and Containers: Problems

d. Bowling Ball = 4,91348 321.56 in3

e. Golf Ball 2.48 in3

f. MLB Baseball = 92 14.14 in3

Sn

5. Medicine Ballsa. Medicine Ball A = 43 (5)3 =

500

3 523.6 in3

b. Medicine Ball B = 43 (5)3 = 500

3 523.6 in3

c. Medicine Ball C = 43 (9.5)3 = 6859

6 3,591.36 in3

d. Medicine Ball D = 43 (8.5)3 = 49136 2,572.44 in3

e. Medicine Ball E = 43 (7.5)3 = 1125

2 1,767.15 in3

It is not possible to make a correlation between size and weight of medicine balls – balls with similar size have very diSerent weights and larger balls sometimes weigh less than smaller ones.

6. Answers may vary. Possible solutions are given.

a. r = 2 in, h = 5 in Volume = 20 62.83 in3

b. r = 5.5 in, h = 2 in Volume = 1212 190.07 in3

c. r = 4 in, h = 9 in Volume = 144 452.39 in3

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Bowlingfx-300ES PLUS sporting equip