Math Problem Statement
Solution
The image shows a right triangle that is being rotated about a horizontal line. The question asks what solid is generated when this right triangle is rotated about the line.
When a right triangle is rotated around its base (as shown in the diagram), the shape formed is a cone. This is because the slanted side of the triangle (the hypotenuse) generates a curved surface, and the base of the triangle becomes the circular base of the cone.
Therefore, the correct answer is:
- Cone
Would you like more details on why the cone is formed or any other aspect of the rotation?
Here are 5 questions related to this problem:
- What solid is formed when a semicircle is rotated about its diameter?
- How is the volume of a cone calculated?
- What happens if a rectangle is rotated about one of its sides?
- Can you generate a cylinder from rotating a triangle?
- How does the axis of rotation affect the type of solid generated?
Tip: Visualizing the rotation of shapes in 3D can help you better understand the resulting solid geometry.
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Math Problem Analysis
Mathematical Concepts
Geometry
Solid of Revolution
3D Shapes
Formulas
Volume of a cone = (1/3) * π * r^2 * h
Theorems
Solid of Revolution Theorem
Suitable Grade Level
Grades 8-10