Curriculum  /  Math  /  10th Grade  /  Unit 6: Three-Dimensional Measurement and Application  /  Lesson 15

Three-Dimensional Measurement and Application

Lesson 15

Math

Unit 6

10th Grade

Lesson 15 of 18

Objective

Use the surface area and volume to solve application problems.

Common Core Standards

Core Standards

  • G.GMD.A.3 — Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
  • G.GMD.B.4 — Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
  • G.MG.A.1 — Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
  • G.MG.A.3 — Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

Foundational Standards

  • 7.G.B.6
  • 8.G.C.9

Criteria for Success

  1. Describe how to find the surface area of cylinders and other prisms using the principle that surface area is just the sum of the area of all the surfaces. 
  2. Use the formulas for the surface area of a cone, $$\pi r^2+\pi r$$ℓ, where $$r$$ is the radius and ℓ is the slant height of the cone, and the surface area of a sphere, $$4\pi r^2$$, to solve problems.
  3. Identify necessary information to solve a problem, and use known quantities to gather that information.
  4. Choose general formulas appropriately to develop a specific formula for finding the surface area or volume, and apply appropriate dimensions. 
  5. Compare surface area of figures by analyzing dimensions and formulas.

Tips for Teachers

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes

Problem 1

Three tennis balls are in a can, each with a diameter of 2.6 inches. 

  1. How much felt is used to cover the three tennis balls?
  2. What is the minimum surface area of the can, including the top and bottom? 

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

The following four packages all contain the same amount of candy. Rank the packages based on the least amount of packaging used to the most amount of packaging used.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

101Questions Dandy Candies

Dandy Candies by is made available on 101Questions under the CC BY 3.0 license. Accessed March 20, 2018, 2:37 p.m..

Modified by Fishtank Learning, Inc.

Target Task

5-10 minutes

What is the surface area and volume of the solid formed by revolving the following two-dimensional figure around the $$y$$-axis?

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include problems such as “an orange that has a diameter of 3 inches is peeled, and the peel is placed on a piece of paper that is 8.5 inches by 11 inches. How much of the paper is not covered by the orange peel?”
  • Include problems such as “a tube of wrapping paper has a diameter of 2 inches and a height of 2 feet. The paper goes around the tube five times. Will you have enough paper to wrap four rectangular prisms that have lengths of 8 inches, heights of 5 inches, and widths of 3 inches? If so, how much wrapping paper will you have left over? If not, how much more will you need?”
  • Include problems where students need to find the partial surface area with one surface missing. 
  • Include problems where one dimension is increased and students are asked to examine the effect on the surface area and the volume. 
  • Include problems where a two-dimensional shape is spun around an axis and students are asked to find the surface area and volume. 

Next

Solve multistep volume and surface area problems with rates and unit conversions.

Lesson 16
icon/arrow/right/large

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Area and Circumference of Circles

Topic B: Three-Dimensional Concepts and General Volume

Topic C: Cavalieri's Principle, Spheres, and Composite Volume

Topic D: Surface Area, Scaling, and Modeling with Geometry

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free