Cross Sections and Solids of Rotation


Related Topics:
Common Core (Geometry)
Common Core for Mathematics




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Videos, examples, solutions, and lessons to help High School students learn how to identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
Common Core: HSG-GMD.B.4

The following figures show some solids of rotation: cone, cylinder, frustum, sphere. Scroll down the page for more examples and solutions.
Solids of Rotation
 

Geometry Cross sections
Examples:
What is the shape of the cross section of each of the following figures?




Solids of rotation (Solids in 3D)
Rotate a triangle to get a cone.
Rotate a rectangle to get a cylinder
Rotate a trapezium to get frustum
Rotate a circle (semi-circle) to get a sphere.

Solids of rotation
A solid of rotation is the three-dimensional (solid) object formed by rotating a two-dimensional area around an axis.

For animations to explore the shapes of two-dimensional cross-sections of three-dimensional objects and identify three-dimensional objects generated by rotations of two-dimensional objects, see: Cross Section and Rotation Animations



Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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