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Chapter 11 builds on your understanding of the area of polygons from Chapter 8 and similarity from Chapter 2 and applies these concepts to 3 dimensional solids. Using your background knowledge you will find both the surface area and volumes of prisms, cones, cylinders and spheres.
Chapter 11 builds on your understanding of the area of polygons from Chapter 8 and similarity from Chapter 2 and applies these concepts to 3 dimensional solids. Using your background knowledge you will find both the surface area and volumes of prisms, cones, cylinders and spheres.
Current Chapter Resources and Practice
Current Chapter Resources and Practice
Background Knowledge Resources
Background Knowledge Resources
Checkpoint Review: Students master different skills at different speeds. No two students learn exactly the same way at the same time. At some point you will be expected to perform certain skills accurately. Most of the Checkpoint problems incorporate skills previously developed. Each chapter has a different skill that should be mastered.
Checkpoint 11: Angle measures and areas of regular polygons
Checkpoint 11: Angle measures and areas of regular polygons
You e-book has a checkpoint resource (you must have the e-book open to access the link and click on CP 11)
Learning Outcomes for Chapter 11: Open your e-book to access the links to the problems
Learning Outcomes for Chapter 11: Open your e-book to access the links to the problems
Previous Content
- Master Checkpoint 11: Angle measures and areas of regular polygons, as in problems 11‑7, 11-31, 11-54, 11-67(b), 11-81, and CL 11-88.
- Understand chord, radii, and angle relationships in circles and use those relationships to solve problems, including calculating the length of a chord or segments formed by intersecting chords, as in problems 10-84, 10-96, 10-108, 11-9, 11-10(c), 11-33, 11-82, CL 11-93(b), and CL 11-94.
- Understand and use the fact that a line tangent to a circle is perpendicular to the radius of the circle at the point of tangency, as in problems 10-108(a) and (b), 11-23, 11-48(a), 11‑72, and CL 11-93(a).
Current Content
- Calculate the surface area and volume (or calculate a missing dimension given the volume) of prisms, as in problems 11-7, 11-22, 11-46, 11-66(a), 11-67(b), and CL 11‑89, and cylinders, as in problems 11-20(a) and (b), 11-56, 11‑67(a), 11-83, 11-85, and CL 11-92.
- Calculate volume and/or area as part of a three-dimensional situation, as in problems 11‑7, 11-22(b), 11-32, 11-67, CL 11-89, and CL 11-90. Problems about volume or surface area may require students to compute the area of polygons using trigonometry. Students could be asked to calculate the volume of a slice of a cylinder, where the base is a sector of a circle.
- Understand and apply the relationship between a linear scale factor and the ratio of areas or ratio of volumes of similar solids, as in problems 11-19, 11-20(c), 11‑30, 11-55, 11-68, and CL 11-96. Students should be able to calculate a ratio of areas or of volumes given a linear scale factor. Students should be able to use the ratios to compute side lengths, surface areas, or volumes of similar solids given measurements of one shape in a pair of similar shapes.
- Compute the volume of a pyramid, as in problems 11-53, 11-69, and CL 11-91, or cone, as in problems 11-66(b), 11-85(b), and CL 11‑92.
- Calculate the total surface area of a pyramid, as in problems 11-45, 11-53, and CL 11‑91, or cone, as in problems 11-66(b) and 11-85(a). Students may find it easier to visualize surface area when they can access a 3‑D model of the shape.
- Calculate the total surface area or volume of a sphere, as in problem 11-80.
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