https://file.aiquickdraw.com/mathbot/file/1725908857162eiof3m8y.jpg

To calculate the surface area of the cone shown in the image, we need to find both the lateral surface area and the base area. The formula for the total surface area \( A \) of a cone is:

\[
A = \pi r (r + l)
\]

Where:
- \( r \) is the radius of the base (given as 16),
- \( l \) is the slant height (given as 23.4).

### Step-by-step calculation:
1. **Base Area**: 
   The area of the circular base is given by:
   \[
   A_{\text{base}} = \pi r^2 = \pi (16)^2
   \]

2. **Lateral Surface Area**:
   The lateral surface area is given by:
   \[
   A_{\text{lateral}} = \pi r l = \pi (16)(23.4)
   \]

Now, let me calculate the surface area.The surface area calculations are as follows:

1. **Base Area**: \( 804.25 \, \text{square units} \)
2. **Lateral Surface Area**: \( 1176.21 \, \text{square units} \)
3. **Total Surface Area**: \( 1980.46 \, \text{square units} \)

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How does the surface area change if the radius of the cone is doubled?
2. What is the surface area of a cone with the same slant height but a smaller base?
3. Can you derive the formula for the surface area of a cone from geometric principles?
4. How does the slant height affect the lateral surface area of the cone?
5. What is the volume of this cone, and how is it related to the surface area?

**Tip**: When solving surface area problems, ensure you distinguish between lateral and total surface area, especially in cones and cylinders.

What is the surface area of the cone with a radius of 16 and a slant height of 23.4?

Learn how to calculate the surface area of a cone with a radius of 16 and a slant height of 23.4. This geometry problem involves applying formulas for the lateral and base surface areas, providing a step-by-step solution suitable for students in Grades 9-12.

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