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
What is the shape of the cross section of each of the following figures?
Learn to identify cross sections of solids.
Sketch and identify the cross section of each of the figure below.
Cross Sections & Rotations of 2D to 3D
A video that shows how you can convert Figures from 2D to 3D by
cross sections and rotations.
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:
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other 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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