To find the surface area of a cone, you can use the following 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.
Given:
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The base diameter of the cone is 25 centimeters, so the radius \( r \) is: \[ r = \frac{25}{2} = 12.5 \text{ cm} \]
-
The slant height \( l \) is given as 22 centimeters.
Now, substituting the values into the surface area formula:
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Calculate the area of the base: \[ \pi r^2 = 3.14 \times (12.5)^2 = 3.14 \times 156.25 = 490.625 \text{ cm}^2 \]
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Calculate the lateral surface area: \[ \pi r l = 3.14 \times 12.5 \times 22 = 3.14 \times 275 = 865.5 \text{ cm}^2 \]
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Add both areas to find the total surface area: \[ \text{Surface Area} = 490.625 + 865.5 = 1356.125 \text{ cm}^2 \]
Therefore, the surface area of the cone is approximately 1,354.125 square centimeters.
The correct answer is 1,354.125 square centimeters.