To find the surface area of a cone, we can 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 of the cone,
- \( \pi \) is approximately 3.14.
Given:
- The diameter of the base is 25 cm, so the radius \( r \) is:
\[ r = \frac{25}{2} = 12.5 , \text{cm} \]
- The slant height \( l \) is given as 22 cm.
Now, we can calculate the surface area step by step.
- Calculate the area of the base:
\[ \text{Base Area} = \pi r^2 = 3.14 \times (12.5)^2 \]
Calculating \( (12.5)^2 \):
\[ 12.5^2 = 156.25 \]
Thus, the base area is:
\[ \text{Base Area} = 3.14 \times 156.25 = 490.625 , \text{cm}^2 \]
- Next, calculate the lateral surface area:
\[ \text{Lateral Surface Area} = \pi r l = 3.14 \times 12.5 \times 22 \]
Calculating \( 12.5 \times 22 \):
\[ 12.5 \times 22 = 275 \]
So, the lateral surface area is:
\[ \text{Lateral Surface Area} = 3.14 \times 275 = 863.5 , \text{cm}^2 \]
- Finally, add the area of the base and the lateral surface area together to get the total surface area:
\[ \text{Total Surface Area} = \text{Base Area} + \text{Lateral Surface Area} = 490.625 + 863.5 \]
Calculating that:
\[ \text{Total Surface Area} = 1354.125 , \text{cm}^2 \]
Thus, the surface area of the cone is \( 1354.125 , \text{cm}^2 \).
The correct response is:
1,354.125 square centimeters.