A rectangle with its base of three units and a height of four units. There is a dashed line, m, that is parallel to the base and intersects rectangle halfway up its height.
What solid 3D object is produced by rotating the rectangle about line 
\[\blue m\]?

When a rectangle is rotated about a line parallel to its base, the resulting 3D object is a **cylinder**.

Here, the rectangle has a base of 3 units and a height of 4 units, with the line \( m \) intersecting it halfway up its height. This line \( m \) is parallel to the base of the rectangle. When the rectangle is rotated about this line, the solid object produced is a **cylinder with a hollow core** (a cylindrical shell), since the rotation is around a line that is not at the edge of the rectangle.

### Characteristics of the 3D object produced:
- **Outer radius:** The outer radius of the cylinder will be half the height of the rectangle, which is \( 2 \) units (since the height is \( 4 \) units and \( m \) is halfway).
- **Inner radius:** The inner radius is \( 0 \) units because the line \( m \) itself is at the center of the rectangle's height.
- **Height of the cylinder:** The height of the cylinder will be the length of the base of the rectangle, which is \( 3 \) units.

Thus, the 3D object is a **solid cylinder with height 3 units and radius 2 units**.

Would you like more details or have any questions? 

Here are 5 relative questions:
1. What is the volume of the cylinder formed by rotating the rectangle about line \( m \)?
2. How does the position of line \( m \) affect the shape of the solid formed?
3. What would happen if the rectangle was rotated about its base instead of the line \( m \)?
4. How would the shape change if the rectangle had a different aspect ratio, such as a square?
5. Can you describe the properties of a cylinder formed by rotating a rectangle about its diagonal?

**Tip:** Visualizing the problem with diagrams or sketches often helps in understanding the geometry of the situation.

Explore the solid 3D object produced by rotating a rectangle with a base of 3 units and a height of 4 units about a line m parallel to its base. Learn about the characteristics of the resulting cylinder, including its height and radius. Suitable for Grades 7-9.

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