Curriculum / Math / 10th Grade / Unit 6: Three-Dimensional Measurement and Application / Lesson 14
Math
Unit 6
10th Grade
Lesson 14 of 18
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Lesson Notes
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Use lateral surface area formulas to solve problems.
The core standards covered in this lesson
N.Q.A.2 — Define appropriate quantities for the purpose of descriptive modeling.
The foundational standards covered in this lesson
7.G.B.6 — Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
8.G.B.7 — Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
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
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?
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.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Write a formula for the lateral surface area of a right circular cone using only the height and radius, as shown below.
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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Use the surface area and volume to solve application 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
N.Q.A.2
G.GMD.A.3G.GMD.B.4G.MG.A.1G.MG.A.3
Solve multistep volume and surface area problems with rates and unit conversions.
G.GMD.A.3N.Q.A.2N.Q.A.3
Apply density concepts to surface area and volume problems.
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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