Curriculum / Math / 10th Grade / Unit 6: Three-Dimensional Measurement and Application / Lesson 16
Math
Unit 6
10th Grade
Lesson 16 of 18
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Lesson Notes
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Solve multistep volume and surface area problems with rates and unit conversions.
The core standards covered in this lesson
G.GMD.A.3 — Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
N.Q.A.2 — Define appropriate quantities for the purpose of descriptive modeling.
N.Q.A.3 — Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
How long will it take to fill the tank?
Water Tank by Dan Meyer is licensed under the CC BY 3.0 license. Accessed June 2, 2017, 5:15 p.m..
Jared is scheduled for some tests at his doctor’s office tomorrow. His doctor has instructed him to drink 3 liters of water today to clear out his system before the tests. Unfortunately, Jared forgot to bring his water bottle to work and was left in the unfortunate position of having to use the annoying paper cone cups that are provided by the water dispenser at his workplace. He measures one of these cones and finds it to have a diameter of 7 centimeters and a slant height of 9.1 centimeters.
Doctor's Appointment, accessed on June 8, 2017, 2:15 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
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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Apply density concepts to surface area and volume problems.
Topic A: Area and Circumference of Circles
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
Calculate and justify composite area and circumference of circles.
N.Q.A.1N.Q.A.2N.Q.A.3
Solve multistep area and circumference of circles problems involving cost and other rates.
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Topic B: Three-Dimensional Concepts and General Volume
Describe the terms point, line, and plane. Define and classify polyhedrons, specifically prisms and pyramids.
G.CO.A.1
Define a general cylinder and general cone. Identify two-dimensional shapes that when revolved will form a cylinder.
G.CO.A.1G.GMD.B.4
Use volume concepts and formulas to analyze and solve multistep problems with cylinders and prisms.
G.GMD.A.1G.GMD.A.3
Define and calculate the volume of pyramids and cones. Describe the relationship between general cylinders and general cones with the same base area.
Use the Pythagorean Theorem to find missing measurements and calculate volume of pyramids, prisms, and compound shapes comprised of pyramids and prisms.
G.GMD.A.3G.GMD.B.4G.SRT.C.8
Topic C: Cavalieri's Principle, Spheres, and Composite Volume
Describe the cross-sections of prisms and cylinders and make conjectures about volume from the cross-sections.
G.GMD.A.3G.GMD.B.4
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.
G.GMD.A.1G.GMD.A.2
Identify cross-sections of pyramids and use the relationships between the cross-sections to determine the volume of truncated cones and pyramids.
G.GMD.A.2G.GMD.A.3
Calculate the volume of a sphere and use this in the solution of problems.
G.GMD.A.1G.GMD.A.2G.GMD.A.3N.Q.A.3
Calculate the volume of compound objects and those with subtracted solids. Determine how the volume will be affected by scaling one or more dimensions.
G.GMD.A.3G.GMD.B.4N.Q.A.3
Topic D: Surface Area, Scaling, and Modeling with Geometry
Use lateral surface area formulas to solve problems.
N.Q.A.2
Use the surface area and volume to solve application problems.
G.GMD.A.3G.GMD.B.4G.MG.A.1G.MG.A.3
G.GMD.A.3N.Q.A.2N.Q.A.3
G.GMD.A.3G.MG.A.2N.Q.A.2N.Q.A.3
Apply constraints on volume, surface area, or cost to solve design problems with three-dimensional figures.
G.GMD.A.3G.MG.A.2G.MG.A.3N.Q.A.2N.Q.A.3
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