Lesson 10 | Three-Dimensional Measurement and Application | 10th Grade Mathematics

Objective

Describe Cavalieri’s principle relating equal area cross-sections and volume, and how this relates to the formulas for volume. Derive the volume of a sphere using Cavalieri’s principle.

Lesson Map

Topic A: Area and Circumference of Circles

Lesson

Describe and use the formulas for area and circumference of circles to solve problems.

Standards

A.SSE.A.1G.GMD.A.1N.Q.A.3

Lesson

Calculate and justify composite area and circumference of circles.

Standards

N.Q.A.1N.Q.A.2N.Q.A.3

Lesson

Solve multistep area and circumference of circles problems involving cost and other rates.

Standards

N.Q.A.1N.Q.A.2N.Q.A.3

Topic B: Three-Dimensional Concepts and General Volume

Lesson

Describe the terms point, line, and plane. Define and classify polyhedrons, specifically prisms and pyramids.

Standards

G.CO.A.1

Lesson

Define a general cylinder and general cone. Identify two-dimensional shapes that when revolved will form a cylinder.

Standards

G.CO.A.1G.GMD.B.4

Lesson

Use volume concepts and formulas to analyze and solve multistep problems with cylinders and prisms.

Standards

G.GMD.A.1G.GMD.A.3

Lesson

Define and calculate the volume of pyramids and cones. Describe the relationship between general cylinders and general cones with the same base area.

Standards

G.GMD.A.1G.GMD.A.3

Lesson

Use the Pythagorean Theorem to find missing measurements and calculate volume of pyramids, prisms, and compound shapes comprised of pyramids and prisms.

Standards

G.GMD.A.3G.GMD.B.4G.SRT.C.8

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

Lesson

Describe the cross-sections of prisms and cylinders and make conjectures about volume from the cross-sections.

Standards

G.GMD.A.3G.GMD.B.4

Lesson

Describe Cavalieri’s principle relating equal area cross-sections and volume, and how this relates to the formulas for volume. Derive the volume of a sphere using Cavalieri’s principle.

Standards

G.GMD.A.1G.GMD.A.2

Lesson

Identify cross-sections of pyramids and use the relationships between the cross-sections to determine the volume of truncated cones and pyramids.

Standards

G.GMD.A.2G.GMD.A.3

Lesson

Calculate the volume of a sphere and use this in the solution of problems.

Standards

G.GMD.A.1G.GMD.A.2G.GMD.A.3N.Q.A.3

Lesson

Calculate the volume of compound objects and those with subtracted solids. Determine how the volume will be affected by scaling one or more dimensions.

Standards

G.GMD.A.3G.GMD.B.4N.Q.A.3

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

Lesson

Use lateral surface area formulas to solve problems.

Standards

N.Q.A.2

Lesson

Use the surface area and volume to solve application problems.

Standards

G.GMD.A.3G.GMD.B.4G.MG.A.1G.MG.A.3

Lesson

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

Standards

G.GMD.A.3N.Q.A.2N.Q.A.3

Lesson

Apply density concepts to surface area and volume problems.

Standards

G.GMD.A.3G.MG.A.2N.Q.A.2N.Q.A.3

Lesson

Apply constraints on volume, surface area, or cost to solve design problems with three-dimensional figures.

Standards

G.GMD.A.3G.MG.A.2G.MG.A.3N.Q.A.2N.Q.A.3

Three-Dimensional Measurement and Application

Objective

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Three-Dimensional Measurement and Application

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Math

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