To find the surface area of a cone, we use the formula:
\[ \text{Surface Area} = \pi r^2 + \pi r l \]
where:
- \( r \) is the radius of the base,
- \( l \) is the slant height (hypotenuse) of the cone.
Step 1: Calculate the radius.
The diameter of the base is given as 25 cm, so the radius \( r \) is:
\[ r = \frac{\text{diameter}}{2} = \frac{25 , \text{cm}}{2} = 12.5 , \text{cm} \]
Step 2: Use the given slant height.
The slant height \( l \) is given as 22 cm.
Step 3: Calculate the surface area.
- Calculate the area of the base:
\[ \text{Area of the base} = \pi r^2 = 3.14 \times (12.5)^2 \]
Calculating \( (12.5)^2 \):
\[ (12.5)^2 = 156.25 \]
Then,
\[ \text{Area of the base} = 3.14 \times 156.25 \approx 490.625 , \text{cm}^2 \]
- Calculate the lateral surface area:
\[ \text{Lateral Surface Area} = \pi r l = 3.14 \times 12.5 \times 22 \]
Calculating \( 12.5 \times 22 \):
\[ 12.5 \times 22 = 275 \]
Then,
\[ \text{Lateral Surface Area} = 3.14 \times 275 \approx 865.5 , \text{cm}^2 \]
Step 4: Combine the areas to find the total surface area.
\[ \text{Total Surface Area} = \text{Area of the base} + \text{Lateral Surface Area} \]
\[ \text{Total Surface Area} \approx 490.625 + 865.5 \approx 1,356.125 , \text{cm}^2 \]
Conclusion:
Given the answer choices, the closest approximation is:
1,354.125 square centimeters (as it may be rounded).
Thus, the correct answer is:
1,354.125 square centimeters.