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 
\[\blue m\]? What is the diameter?


When you rotate a rectangle around a line parallel to one of its sides, the shape generated is a **cylinder**.

### Given:
- Base of the rectangle = 3 units
- Height of the rectangle = 4 units
- Line \( m \) is parallel to the base and intersects the rectangle halfway up its height.

### Rotating the Rectangle:
- The line \( m \) divides the rectangle into two equal parts, each with a height of 2 units (since the total height is 4 units and the line is halfway up).
- When the rectangle is rotated about line \( m \), the height of the cylinder will be equal to the base of the rectangle, which is 3 units.
- The radius of the cylinder will be half of the height of the rectangle, which is 2 units.

### Diameter of the Cylinder:
The diameter of the cylinder is twice the radius, so:
\[
\text{Diameter} = 2 \times 2 \, \text{units} = 4 \, \text{units}
\]

### Summary:
- **Solid 3D Object:** Cylinder
- **Diameter of the Cylinder:** 4 units

Would you like more details on this concept or have any questions?

---

Here are 5 related questions to consider:
1. What would happen if the line \( m \) was closer to the base rather than halfway up?
2. How would the cylinder's properties change if the rectangle's dimensions were different?
3. What shape would be produced if the rectangle were rotated about one of its sides instead?
4. What is the volume of the cylinder generated in this scenario?
5. How does the diameter of the cylinder relate to the original dimensions of the rectangle?

**Tip:** In problems involving rotation of shapes, always consider the axis or line of rotation carefully to determine the resulting 3D object's dimensions.

Explore how a rectangle with a base of 3 units and a height of 4 units, rotated around a line parallel to its base, forms a cylinder. Learn about the properties of the resulting cylinder, including its diameter of 4 units. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation