Three-Dimensional Measurement and Application

Lesson 14

Math

Unit 6

10th Grade

Lesson 14 of 18

Objective


Use lateral surface area formulas to solve problems.

Common Core Standards


Core Standards

  • N.Q.A.2 — Define appropriate quantities for the purpose of descriptive modeling.

Foundational Standards

  • 7.G.B.6
  • 8.G.B.7

Criteria for Success


  1. Define the lateral surface area of three-dimensional figures as the surface area of the figure without the base(s).
  2. Choose general formulas appropriately to develop a specific formula for finding the lateral surface area, and apply appropriate dimensions.
  3. Describe how the formulas for the lateral surface area relate to the surface area of the whole three-dimensional figure.

Tips for Teachers


  • This lesson will prepare students to access G-MG.1 and G-MG.3 standards in the next lesson by discussing and reviewing surface area of three-dimensional figures. 
  • Have students use or develop a reference sheet as needed. A good example is the Massachusetts Comprehensive Assessment System Grade 10 Mathematics Reference Sheet.
  • Some of the Problem Set Guidance is from Grade 7 (7.G.6). However, these questions will help the students build procedural fluency with lateral surface area through their conceptual understanding of three-dimensional figures. 
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Anchor Problems


Problem 1

Below is a right circular cylinder with a 4-inch diameter and $$6\frac{3}{4}$$ inch height.

If you want to cover the outside of the can with one label with no overlaps or gaps, what shape and dimensions must the label be?

Guiding Questions

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Problem 2

Below are formulas for finding the lateral surface area of three-dimensional shapes. Match the appropriate shape with the formula, and describe each component of the formula in terms of dimensions of the shape.

Right rectangular prism $$LA=2s$$â„“
Right square pyramid $$LA=2\pi r h$$
Right circular cylinder $$LA=2(hw)+2(lh)$$
Right circular cone $$LA=\pi r $$â„“

Guiding Questions

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Target Task


Write a formula for the lateral surface area of a right circular cone using only the height and radius, as shown below.

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.

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Lesson 13

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Lesson 15

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

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