https://file.aiquickdraw.com/mathbot/file/1729620384081v763a6fu.jpg

The problem asks to calculate the curved surface area of a cone using the formula:

\[
\text{Curved surface area} = \pi r l
\]

where:
- \( r \) is the radius of the base, and
- \( l \) is the slant height.

### Given values:
- Diameter of the cone's base = 6 cm, so the radius \( r \) is:
  \[
  r = \frac{\text{diameter}}{2} = \frac{6}{2} = 3 \, \text{cm}
  \]
- Slant height \( l = 23 \, \text{cm} \).

### Step-by-step calculation:
1. **Substitute** the values into the formula:
   \[
   \text{Curved surface area} = \pi \times 3 \times 23
   \]
   \[
   \text{Curved surface area} = 69\pi
   \]

2. **Approximate using** \( \pi \approx 3.1416 \):
   \[
   69 \times 3.1416 \approx 216.769 \, \text{cm}^2
   \]

3. **Round to the nearest integer**:
   \[
   \text{Curved surface area} \approx 217 \, \text{cm}^2
   \]

### Final Answer:
The curved surface area of the cone is **217 cm²**.

Would you like further explanation or details on any step? Here are some related questions for further exploration:

1. How do you find the total surface area of the cone, including the base?
2. What is the volume of this cone?
3. How does changing the slant height affect the curved surface area?
4. How would the area change if the diameter were doubled?
5. What is the significance of the slant height in the cone's geometry?

**Tip**: Always ensure you're using the correct units throughout calculations to avoid errors.

The cone below has a slant height of 23 cm and a diameter of 6 cm. Work out the curved surface area of the cone. Give your answer to the nearest integer and remember to give the correct units.

Learn how to calculate the curved surface area of a cone with a slant height of 23 cm and a base diameter of 6 cm. This problem uses the formula πrl to find the curved surface area. Suitable for students in Grades 7-10.

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