# MA.7.GR.2.2

Solve real-world problems involving surface area of right circular cylinders.

### Clarifications

Clarification 1: Within this benchmark, the expectation is not to memorize the surface area formula for a right circular cylinder or to find radius as a missing dimension.

Clarification 2: Solutions may be represented in terms of pi (π) or approximately.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Geometric Reasoning
Status: State Board Approved

## Benchmark Instructional Guide

### Terms from the K-12 Glossary

• Cylinder (Circular)
• Pi (π)
• Surface Area

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grade 6, students found the area of quadrilaterals and composite figures by decomposing them into triangles or rectangles, which developed into finding the surface area of right rectangular prisms and right rectangular pyramids using a figure’s net. In grade 7, students find the surface area of a right circular cylinder using the figure’s net and build that into solving real-world problems involving surface area of right circular cylinders. In high school, students will solve mathematical and real-world problems involving the surface area of cylinders, pyramids, prisms, cones and spheres.
• Instruction includes finding the height or the circumference (working backwards) when given the surface area of a right circular cylinder, but students will not be expected to find the radius as a missing dimension (MTR.3.1).

### Common Misconceptions or Errors

• Students often confuse the vocabulary base, length, height and “B” (base area), when moving between two-and three-dimensional figures. To address this misconception, continue to use the parts of the net to calculate the surface area, rather than focusing on the formula.
• Students may incorrectly believe that whatever is lying flat is the base of the figure. To address this misconception, remind students that while a cylinder may lay on its side, the bases are the circles with the height being the perpendicular distance between them. Provide multiple orientations of objects and continue to break them down to their nets.

### Strategies to Support Tiered Instruction

• Instruction includes the use of geometric software to allow students to explore the difference between base, length, height and “$B$” (base area).
• Teacher creates and posts an anchor chart with visual representations of a right circular cylinder to assist in correct academic vocabulary when solving real-world problems.
• Teacher provides students with an example of a three-dimensional figure in its original position then provides multiple orientations to discuss how the location of the figure’s base changes, but the dimensions of the figure do not change.
• For example, two right circular cylinders are shown below with the same dimensions but in different orientations. The base is highlighted in each.

• Teacher models a visual of a three-dimensional figure and its dimensions in the context of a real-world problem.
• Instruction includes opportunities for students to solve for the surface area of a given right circular cylinder in terms of pi before replacing the value of pi with an approximation to determine the estimated surface area.
• Instruction includes color-coding and labeling the dimensions of a right circular cylinder.
• Teacher provides instruction focused on manipulatives or geometric software for students to develop understanding of the difference between the formulas for area, surface area and volume.
• Teacher provides opportunities for students to comprehend the context or situation by engaging in questions (laminating these questions on a printed card for students to utilize as a resource in and out of the classroom would be helpful).
• What do you know from the problem?
• What is the problem asking you to find?
• Can you create a visual model to help you understand or see patterns in your problem?
• Teacher encourages students to continue to use the parts of the net to calculate the surface area, rather than focusing on the formula.
• Teacher reminds students that while a cylinder may lay on its side, the bases are the circles with the height being the perpendicular distance between them. Provide multiple orientations of objects and continue to break them down to their nets.

The Fine Arts Club will be making and selling a soda can snuggie for a fundraiser. They researched the dimensions of a standard soda can to be 4.83 inches high with a diameter of 2.13 inches across the top and 2.6 inches at the widest part of the can. A soda snuggie that will keep the soda cold will require an insulated layer, a liner and a decorative outer fabric.
• Part A. Provide a design the Fine Arts Club could use to make their soda snuggie. How much of each material will be needed for each soda snuggie?

• Part B. Compare your design with a partner (or group). What are the similarities? What changes (if any) would you make to your design based on the ideas of others?

### Instructional Items

Instructional Item 1
A cosmetics company is selling a new line of lipstick and needs to determine how much plastic is needed to wrap each cylindrical tube. If the lipstick tube is 12.1 millimeters (mm) in diameter with a length of 72 mm, how many mm2 of plastic is needed for one tube? How much will be needed for a box of 24?

Instructional Item 2
Melanie is buying a candle for a gift. She has 80.07 in2 of wrapping paper and all of the candles she is looking at have a radius of 1.5 in. What height candle can Melanie buy if she uses all of the wrapping paper she has?

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

## Related Courses

This benchmark is part of these courses.
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.7.GR.2.AP.2: Given the formula, use tools to find the surface area of a right circular cylinder using the figure’s net.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Lesson Plans

Students will apply skills from the Geometry Domain to build graduation caps for themselves using heavyweight poster paper. They will also apply some basic mathematical skills to determine dimensions and to determine minimum cost. Some of the Geometric skills reinforced in Building Graduation Caps: Cooperative Assignment are finding area, applying the concept of similarity, and the application of the properties of parallelograms. Other skills also involved in this application are measuring, and statistical calculations, such as finding the mean and the range. In addition to the hands-on group project that takes place during the lesson, there is the Prerequisite Skills Assessment: Area that should be administered before the group activity and a home-learning activity. Building Graduation Caps: Individual Assignment is the home-learning assignment; it is designed to reinforce the skills learned in the group activity.

Type: Lesson Plan

How Much Surface Area Does Your Skin Take Up?:

Students relate their body parts to six cylinders. They adjust the surface area of a cylinder formula, and then measure, record, and compute the approximate surface area of their skin. Students will develop a better understanding of how much skin covers up their body when they calculate how much surface area their skin takes up.

Type: Lesson Plan

Relating Surface Area and Volume:

Students will recognize that while the surface area may change, the volume can remain the same. This lesson is enhanced through the multimedia CPALMS Perspectives Video, which introduces students to the relationship between surface area and volume.

Type: Lesson Plan

Shipping Rolled Oats:

Students should think of different ways the cylindrical containers can be set up in a rectangular box. Through the process, students should realize that although some setups may seem different, they result in a box with the same volume. In addition, students should come to the realization (through discussion and/or questioning) that the thickness of a cardboard box is very thin and will have a negligible effect on the calculations.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Shipping Rolled Oats:

Students should think of different ways the cylindrical containers can be set up in a rectangular box. Through the process, students should realize that although some setups may seem different, they result in a box with the same volume. In addition, students should come to the realization (through discussion and/or questioning) that the thickness of a cardboard box is very thin and will have a negligible effect on the calculations.