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We are tasked with finding the height of the cone-shaped door stopper, given its volume and radius.

The formula for the volume of a cone is:

\[
V = \frac{1}{3} \pi r^2 h
\]

### Given:
- \( V = 267\pi \, \text{cm}^3 \)
- \( r = 14 \, \text{cm} \)

### Step 1: Plug in the known values
\[
267\pi = \frac{1}{3} \pi (14)^2 h
\]

### Step 2: Simplify the equation
\[
267\pi = \frac{1}{3} \pi (196) h
\]

\[
267\pi = \frac{196\pi}{3} h
\]

### Step 3: Cancel out \( \pi \) from both sides
\[
267 = \frac{196}{3} h
\]

### Step 4: Solve for \( h \)
Multiply through by 3 to eliminate the fraction:
\[
3 \times 267 = 196h
\]

\[
801 = 196h
\]

Divide both sides by 196:
\[
h = \frac{801}{196}
\]

\[
h \approx 4.1 \, \text{cm} \, (\text{to 1 decimal place})
\]

### Final Answer:
The height of the door stopper is approximately **4.1 cm**.

---

Would you like a step-by-step explanation or details about related concepts?  
Here are 5 additional questions that build on this problem:  
1. What is the relationship between the volume of a cone and its radius?  
2. How would the height change if the radius were doubled while keeping the volume constant?  
3. What are the units of the volume of a cone, and how are they derived?  
4. How does the formula for the volume of a cone compare to that of a cylinder?  
5. What are some practical applications of the cone volume formula?  

**Tip:** Always check your units when solving geometry problems to ensure consistency!

Calculate the height of a cone-shaped door stopper given that its radius is 14 cm and its volume is 267π cm³. Provide the answer to 1 decimal place.

Learn how to calculate the height of a cone-shaped object given its radius and volume using the formula V = (1/3)πr²h. This geometry problem is suitable for Grades 8-10 and includes step-by-step calculations.

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