Dimensions of Cross Sections Using Similarity
Dimensions of Cross Sections Using Similarity is a Grade 7 math skill in Reveal Math Accelerated, Unit 12: Area, Surface Area, and Volume, where students use the properties of similar figures to determine the dimensions of a cross section of a 3D solid by setting up proportions based on the relationship between the cross section and the overall figure. This applies similarity reasoning to three-dimensional geometry.
Key Concepts
When a pyramid or cone is sliced by a plane parallel to its base, the resulting cross section is similar to the base. The dimensions of the cross section can be found using the linear scale factor, which is the ratio of the distance from the vertex to the total height:.
$$\frac{d c}{d b} = \frac{h c}{h t}$$.
Common Questions
How do you use similarity to find the dimensions of a cross section?
Identify the ratio between the position of the cross section and the total height or length of the solid. Set up a proportion using corresponding dimensions of the cross section and the full figure, then solve for the unknown dimension.
What shape is a cross section typically?
A cross section is the flat shape exposed when a 3D solid is cut by a plane. Cross sections of pyramids parallel to the base are similar to the base, and those of cylinders parallel to the base are circles.
Why are cross sections of pyramids and cones similar to their bases?
When a pyramid or cone is cut by a plane parallel to the base, the resulting cross section has the same shape as the base but smaller. The scale factor depends on how far the cut is from the apex relative to the total height.
What is Reveal Math Accelerated Unit 12 about?
Unit 12 covers Area, Surface Area, and Volume, including circle geometry, cross sections, surface areas of 3D figures, cube roots, and volume applications.