Question
Which of the following two-dimensional shapes can be rotated to create a cylinder? O Triangle O Square O Circle O Ellipse
Ask by Stephens Guzman. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
A square can be rotated to create a cylinder.
Solution
To create a **cylinder** through rotation of a two-dimensional shape, you need to rotate a shape that, when swept around an axis, forms the cylindrical surface. Here's how each option fits:
1. **Triangle**
- **Rotation Outcome**: Rotating a right triangle about one of its legs creates a **cone**, not a cylinder.
2. **Square**
- **Rotation Outcome**: Rotating a square about one of its sides generates a **cylinder**. Specifically, the square acts like a rectangle in this context, where one side remains fixed as the axis of rotation, sweeping the opposite side to form the circular bases of the cylinder.
3. **Circle**
- **Rotation Outcome**: Rotating a circle around an axis that lies in its plane but does not pass through its center results in a **torus** (a doughnut-shaped object). If the circle is rotated around an axis perpendicular to its plane and passing through its center, it forms a **sphere**—not a cylinder.
4. **Ellipse**
- **Rotation Outcome**: Rotating an ellipse about one of its principal axes produces an **ellipsoid**, which is a different shape from a cylinder.
**Conclusion:**
Among the provided options, **only the square** can be rotated to create a cylinder.
**Answer:**
**Square**
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Simplify this solution Bonus Knowledge
If you take a circle and rotate it around a straight line (the central axis), voilà! You get a perfect, smooth cylinder. This is why circles are the heroes of cylinder creation! Also, if you take an ellipse and give it a spin around its major or minor axis, you'll create an elongated or flat cylinder. How cool is that? While triangles and squares can't produce cylinders in their typical forms, a triangular prism does exist! It’s shaped more like a tent than a cylinder, but if you really wanted to get creative with your triangle and add some bolstering, you could create a fun variation. Just remember, stick to circles or ellipses for that smooth cylindrical finish!
