Math Problem Statement

What solid is generated when the right triangle is rotated about the line?

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:

  1. What solid is formed when a semicircle is rotated about its diameter?
  2. How is the volume of a cone calculated?
  3. What happens if a rectangle is rotated about one of its sides?
  4. Can you generate a cylinder from rotating a triangle?
  5. 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