11-7 Areas and Volumes of Similar Solids
Objective
To compare and find the areas and volumes of similar solids
Lesson Vocabulary
- similar solids
Essential Understanding You can use ratios to compare the areas and volumes of similar solids.
Similar solids have the same shape, and all their corresponding dimensions are proportional. The ratio of corresponding linear dimensions of two similar solids is the scale factor. Any two cubes are similar, as are any two spheres.
Problem 1 Identifying Similar Solids
Plan
How do you check for similarity?
Check that the ratios of the corresponding dimensions are the same. A rectangular prism has three dimensions (l, w, h), so you must check three ratios.
Are the two rectangular prisms similar? If so, what is the scale factor of the first figure to the second figure?
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The prisms are similar because the corresponding linear dimensions are not proportional.
The scale factor is
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The prisms are not similar because the corresponding linear dimensions are proportional.
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs