



9. A well of diameter 150 cm has a stone parapet around it. If the length of the outer edge of the parapet is 616 cm, find the width of the parapet.




To solve this problem, we need to find the width of the parapet around the well.

### Step 1: Understanding the problem
- The **diameter of the well** (inner circle) is 150 cm.
- The **length of the outer edge** of the parapet (which is the circumference of the outer circle) is 616 cm.

### Step 2: Calculate the radius of the well
The radius \( r_1 \) of the well can be found using the diameter:
\[
r_1 = \frac{\text{Diameter}}{2} = \frac{150 \text{ cm}}{2} = 75 \text{ cm}
\]

### Step 3: Find the radius of the outer edge of the parapet
The circumference of the outer edge (outer circle) is given as 616 cm. We can use the circumference formula to find the radius \( r_2 \) of the outer circle:
\[
C = 2\pi r_2
\]
\[
616 = 2\pi r_2
\]
\[
r_2 = \frac{616}{2\pi} = \frac{616}{2 \times 3.1416} \approx \frac{616}{6.2832} \approx 98 \text{ cm}
\]

### Step 4: Calculate the width of the parapet
The width of the parapet is the difference between the radius of the outer circle and the radius of the well:
\[
\text{Width of the parapet} = r_2 - r_1 = 98 \text{ cm} - 75 \text{ cm} = 23 \text{ cm}
\]

So, the width of the parapet is **23 cm**.

Would you like a more detailed explanation or have any further questions? Here are some related questions you might find interesting:

1. What would be the width of the parapet if the diameter of the well was 200 cm and the outer edge was 770 cm?
2. How would the width of the parapet change if the circumference of the outer edge was doubled?
3. If the outer edge circumference was given in meters, how would you approach the problem?
4. What if the well was a square with a side length of 150 cm, how would you find the width of the parapet around it?
5. How does the area of the parapet relate to its width?

**Tip:** When dealing with circular structures, always remember that the circumference directly gives insights into the radius, and small differences can significantly impact other measurements!

Learn how to calculate the width of a parapet around a well with a detailed step-by-step solution. Given the diameter of the well and the length of the outer edge of the parapet, find the width of the parapet. Suitable for high school students studying geometry.

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