Cross Sections and Solids of Rotation
Related Topics:
Common Core (Geometry)
Common Core for Mathematics
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.
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
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