https://file.aiquickdraw.com/mathbot/file/1727808215187gd6bq2m9.jpg

To solve this problem, we need to calculate the total surface area of the cone.

### Step 1: Identify Given Values
- Diameter of the base: \( 46 \, \text{cm} \)
- Radius \( r \) (since radius is half of the diameter): 
  \[
  r = \frac{46}{2} = 23 \, \text{cm}
  \]
- Slant height \( l = 47 \, \text{cm} \)

### Step 2: Formula for Total Surface Area of a Cone
The total surface area of a cone consists of two parts:
1. **Curved surface area (CSA)**: \( \pi r l \)
2. **Base area**: \( \pi r^2 \)

So, the total surface area \( A \) is given by:
\[
A = \pi r l + \pi r^2
\]
This can be factored as:
\[
A = \pi r (l + r)
\]

### Step 3: Substitute the Given Values
We know \( r = 23 \, \text{cm} \) and \( l = 47 \, \text{cm} \), so:
\[
A = \pi \times 23 \times (47 + 23) = \pi \times 23 \times 70
\]

### Step 4: Calculate the Area
First, calculate the product inside the parentheses:
\[
23 \times 70 = 1610
\]

Now, multiply by \( \pi \) (using \( \pi \approx 3.1416 \)):
\[
A = 3.1416 \times 1610 \approx 5057.1 \, \text{cm}^2
\]

### Final Answer:
The total surface area of the cone is approximately **5057.1 cm²**, correct to 1 decimal place.

Would you like any further clarification or details on this solution?

### Related Questions:
1. How do you calculate the volume of this cone?
2. What is the lateral (curved) surface area without the base?
3. How would the total surface area change if the diameter was doubled?
4. Can you derive the slant height formula if only the height and radius were given?
5. How does surface area scale if both dimensions (radius and slant height) are scaled proportionally?

### Tip:
For cone problems, remember that slant height is key to calculating the curved surface area, while the base area relies only on the radius.

Calculate the total surface area of a cone with a diameter of 46 cm and a slant height of 47 cm. Give your answer correct to 1 decimal place.

Learn how to calculate the total surface area of a cone with a diameter of 46 cm and a slant height of 47 cm. This step-by-step guide uses the formula A = πr(l + r) to find the surface area, including curved and base areas. Suitable for students in Grades 9-11.

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