What 3 dimensional shape is created when this shape is rotated around the axis

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
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What 3 dimensional shape is created when this shape is rotated around the axis?

### Rotating Shapes to Create 3D Objects

**Question:** What 3-dimensional shape is created when this shape is rotated around the axis?

(Image Description: There is a blue square with a dashed line beneath it, indicating an axis. An arrow is depicted circling around the axis.)

**Answer Options:**
1. Rectangular prism
2. Cone
3. Cylinder
4. Sphere

### Explanation:

When a 2-dimensional shape like a square is rotated around an axis, it forms a 3-dimensional shape. In this particular case, the blue square is rotated around the vertical dashed line (axis). As you imagine this rotation, picture the square sweeping out a volume in space.

#### Analysis of Options:
- **Rectangular Prism:** This shape is formed by stacking rectangles, not by rotating.
- **Cone:** A cone is formed by rotating a right triangle around one of its legs, not a square.
- **Cylinder:** When a square is rotated around one of its axes, it forms a cylindrical shape because the rotation creates two parallel circular bases connected by the surface that was the square.
- **Sphere:** A sphere is created by rotating a circle around its diameter, not a square.

Thus, the correct answer is **Cylinder**. 

This transformation is crucial in understanding how 2D shapes relate to 3D solids, a fundamental concept in both geometry and real-world applications such as engineering and design.
Transcribed Image Text:### Rotating Shapes to Create 3D Objects **Question:** What 3-dimensional shape is created when this shape is rotated around the axis? (Image Description: There is a blue square with a dashed line beneath it, indicating an axis. An arrow is depicted circling around the axis.) **Answer Options:** 1. Rectangular prism 2. Cone 3. Cylinder 4. Sphere ### Explanation: When a 2-dimensional shape like a square is rotated around an axis, it forms a 3-dimensional shape. In this particular case, the blue square is rotated around the vertical dashed line (axis). As you imagine this rotation, picture the square sweeping out a volume in space. #### Analysis of Options: - **Rectangular Prism:** This shape is formed by stacking rectangles, not by rotating. - **Cone:** A cone is formed by rotating a right triangle around one of its legs, not a square. - **Cylinder:** When a square is rotated around one of its axes, it forms a cylindrical shape because the rotation creates two parallel circular bases connected by the surface that was the square. - **Sphere:** A sphere is created by rotating a circle around its diameter, not a square. Thus, the correct answer is **Cylinder**. This transformation is crucial in understanding how 2D shapes relate to 3D solids, a fundamental concept in both geometry and real-world applications such as engineering and design.
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