Designing and Energy Drink Can Assessment Solutions Page 1 of 10

Designing an Energy Drink Can Cylinders - Volume & Surface Area

Assessment:

1. What is the volume of the cylinder shown at the right?

A. 14π cubic inches B. 48π cubic inches C. 72π cubic inches D. 288π cubic inches

2. What is the surface area of the cylinder shown at the right?

A. 14π square inches B. 44π square inches C. 48π square inches

D. 66π square inches

3. Approximate the volume of an oil tanker railroad car that has a tank that is roughly 12 feet tall and 45 feet long?

A. 2,000 cubic feet B. 5,000 cubic feet C. 6,500 cubic feet D. 20,000 cubic feet

6 in.

6 in.

8 in.

8 in.

Designing and Energy Drink Can Assessment Solutions Page 2 of 10

4. Find the surface area of a hockey puck that is

3 inches in diameter and one inch in height.

A. 9.4 square inches B. 10.4 square inches

C. 19.8 square inches

D. 23.6 square inches

5. Which of the two actions (changing height or changing radius) affects the volume of a given cylinder the most?

A. The cylinder’s height affects the cylinders volume more. B. The cylinder’s radius affects the cylinder’s volume more.

C. When either the height or radius increases, then the other must decrease

by the same amount. Therefore neither one affects the cylinder’s volume.

D. The height and the radius of a cylinder have an equal affect on the cylinder’s volume.

6. If four equal-height cylinders are arranged into an order from smallest to largest radius, then what can you determine about the relationship between their radii and their surface areas?

A. All four have the same surface area. Therefore there is no relationship between length of radius and surface area.

B. A linear relationship occurs between the length of the radius and the

surface area of the entire cylinder.

C. A non-linear relationship occurs between the length of the radius and the surface area of the entire cylinder.

D. As the length of the radius gets larger, then the volume of the cylinder gets

smaller.

Designing and Energy Drink Can Assessment Solutions Page 3 of 10

7. Many common household batteries are cylindrical. These batteries contain a chemical in fluid form called alkaline. If a “C” size battery and a “AA” size battery each have the same height but different diameters, then we can determine a ratio that describes the amount of alkaline within each battery relative to the other. The larger battery (C) has a diameter twice as large as the smaller battery (AA). Both batteries have the same height. Determine the amount of alkaline in the larger battery as a multiple of the amount of alkaline in the smaller battery. Show all steps needed to find this amount.

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ The larger battery has _________ times as much alkaline within it as the smaller battery.

Designing and Energy Drink Can Assessment Solutions Page 4 of 10

8. A large restaurant-sized can of soup is cylindrical with a diameter of 22 cm and a height of 28 cm. This large can of soup will be used to fill small cylindrical bowls. Each small soup bowl has a diameter of 15 cm. and will be filled to a depth of 6 cm. Determine how many cylindrical bowls can be filled with the amount of soup contained in the large can. Show all steps needed to determine your solution.

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ The large can of soup can fill _____ bowls to a depth of 6 cm.

Designing and Energy Drink Can Assessment Solutions Page 5 of 10

9. A wire manufacturer will often start with a thick piece of copper, then stretch it into a longer and thinner piece of wire. If a manufacturer starts with a cylindrical piece of copper that has a diameter of 40 mm and a length of 200 mm, determine how long will a new stretched out piece of copper wire becomes that is to have a diameter of just 4 mm? Show all steps necessary to determine the new length of the thin wire.

10.

______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ The new thin wire will have a length of _____________ mm.

Designing and Energy Drink Can Assessment Solutions Page 6 of 10

10. You’re the project leader for a team of packaging consultants. Your task is to create a new drink can that will double the volume of the original can used for Can O’ Caffeine energy drink. The dimensions of the original can are shown below along with three new options intended to double the volume with the least amount of additional aluminum needed for the new can. As project leader, you are to determine which of the following three options your team cannot considered and state why?

Option A Option B Option C

Option A doubles the diameter while keeping

the height the same.

Option B doubles the height while keeping the

diameter the same.

Option C simply packages two of the original sized cans

together with plastic. Determine which two of the three options listed above does not meet the requirement of doubling the volume with the least amount of additional aluminum.

• Clearly state your reasoning and the necessary calculations to support your findings. Show all steps needed to support your answer. Be sure to include support for both options not meeting the requirements of doubling

the volume with the least amount of additional aluminum.

Can O’ Caffeine

The original can is 6 cm diameter and 10 cm in height.

TWINS

Designing and Energy Drink Can Assessment Solutions Page 7 of 10

10. (con’t)

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

The two options that can’t be used are ___ and ____.

Designing and Energy Drink Can Assessment Solutions Page 8 of 10

Designing an Energy Drink Can Cylinders - Volume & Surface Area

Assessment Solutions Cylinders Assessment Grading Rubric

Multiple Choice: (1 point each

1. A- Uses only sum of diameter & height times π B- Uses only the product of diameter & height times π C- CORRECT D- Uses diameter squared rather than radius squared in volume formula

2. A- Uses only sum of diameter & height times π B- Squares the diameter instead of the radius, then multiplies only by the height. Also omits the bottom of the cylinder. C- Uses only the product of diameter & height times π D. CORRECT

3. A- Finds only the product of π, length, and diameter B- CORRECT C- Rounds the length up before computing volume while keeping π at 3.14 D- Volume found using squared diameter rather than radius

4. A- Finds volume instead of SA by using diameter only times height. B- Finds volume instead of SA by using diameter and adds only the height C- Adds the first two responses together D- CORRECT

5. B - CORRECT

6. C - CORRECT7. 2-point response: The student shows understanding of how change in one

dimension affects volume of a cylinder by doing the following:

• determines that there must be 4 times as much alkaline within the larger battery by comparing volumes.

• uses the correct formula for the volume of a cylinder for each of the two battery sizes.

1-point response: Student does one of the following: • determines that there must be 4 times as much alkaline within the larger

battery by comparing volumes. • uses the correct formula for the volume of a cylinder for each of the two

battery sizes. 0-point response: The student shows very little or no understanding of the

change in one attribute affects the volume of a cylinder.

Designing and Energy Drink Can Assessment Materials Page 9 of 10

8. 2-point response: The student shows understanding of the relationship between

the change in one or two linear dimensions and the corresponding change in volume of a cylinder by doing the following:

• determines that there can be 10 bowls of soup in the large can.

• Compares the volume of the large can (3000π cu. cm. = 9424.8 cu. cm.) to the volume of the soup bowl (337.5 π cu. cm. = 1060.3 cu. Cm

1-point response: Student does one of the following:

• The student determines that there can be 10 bowls of soup in the large can.

• The volumes of the large can (3000π cu. cm. = 9424.8 cu. cm.) and the soup bowl (337.5 π cu. cm. = 1060.3 cu. cm.) are both compared to each other.

0-point response: The student shows very little or understanding of the relationship between the change in one or two linear dimensions and corresponding change in volume of a cylinder.

9. 2-point response: The student shows understanding of the relationship between

the change in one or two linear dimensions and the corresponding change in volume of a cylinder by doing the following:

• determines that the thin wire will be 20,000 mm long.

• shows work using the original volume of the original copper (20,000 π cubic mm = 251,000 cubic mm) equivalent to the volume of the thin wire (4 π × length).

1-point response: The volume of the copper is shown to be 20,000π, but without the correct comparison to a formula for the thin copper wire.

0-point response: The student shows very little or no understanding of the relationship between the change in one or two linear dimensions and corresponding change in volume of a cylinder.

Designing and Energy Drink Can Assessment Materials Page 10 of 10

10. 4-point response: The student shows understanding of the relationship between the change in one or two linear dimensions and corresponding change in volume and surface area of a cylinder by doing the following:

• Option A and Option C are clearly stated as the two that must be eliminated.

• Support includes volume and/or surface area computations for all three options.

• Option A must be eliminated because the doubled radius results in 4 times as much volume.

• Option C must be eliminated because it doubles the volume, but also doubles the surface area.

3-point response: The student does the following:

• states that both Option A and Option C must be eliminated.

• support includes volume and/or surface area computations for all three options.

• does not analyze Option A in enough detail to show that that its volume is 4 times the original amount rather than only the desired 2 times.

2-point response: The student does the following: • states that either Option A or Option C is one of the two that must be

eliminated, but not both.

• support includes volume and/or surface area computations for two of the three options.

• does not analyze Option A in enough detail to show that that its volume is 4 times the original amount rather than only the desired 2 times..

1-point response: The student does the following:

• states that either Option A or Option C is one of the two that must be eliminated, but not both.

• computations are not included to support their response.

• does not analyze Option A in enough detail to show that that its volume is 4 times the original amount rather than only the desired 2 times.

0-point response: The student shows very little or no understanding of the relationship between the change in one or two linear dimensions and corresponding change in volume and surface area of a cylinder.