 
2 pi r cubed equals pi r squared h2πr3=πr2h


The equation you've provided seems to be a mathematical expression that equates two different volumes. Let's analyze it step by step:

### Equation:
\[ 2\pi r^3 = \pi r^2 h \]

### Simplifying the Equation:

1. **Cancel out \(\pi\) from both sides** (assuming \(\pi \neq 0\)):
   \[
   2r^3 = r^2 h
   \]

2. **Divide both sides by \(r^2\)** (assuming \(r \neq 0\)):
   \[
   2r = h
   \]

### Final Relationship:
The equation simplifies to:
\[ h = 2r \]

This means that the height \(h\) is twice the radius \(r\).

### Interpretation:
This relationship might describe a specific geometric shape or situation, where the height is twice the radius. One possible interpretation could be a cylinder where this condition holds.

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Would you like more details or have any questions?

Here are 5 related questions to explore:

1. How does the volume of a cylinder relate to its height and radius?
2. What geometric shapes have similar volume relations as described in the equation?
3. How would this relationship change if \(h = 3r\) instead?
4. How does the surface area of a cylinder compare to its volume?
5. What other shapes have volumes involving \(\pi r^3\)?

**Tip:** When dealing with equations involving \(\pi\), it's often useful to cancel \(\pi\) if it appears on both sides, simplifying the expression.

Explore the equation 2πr³ = πr²h and its implications. Learn how to simplify and interpret this relationship, where the height h is twice the radius r. This problem involves geometry and volume calculations of solids, suitable for Grades 7-9.

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