To find the surface area of the cone, we need to calculate both the lateral surface area and the base area.
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Find the radius of the base: \[ \text{Radius} (r) = \frac{\text{Diameter}}{2} = \frac{25 \text{ cm}}{2} = 12.5 \text{ cm} \]
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Calculate the base area: \[ \text{Base Area} = \pi r^2 = 3.14 \times (12.5)^2 = 3.14 \times 156.25 = 490.625 \text{ cm}^2 \]
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Calculate the lateral surface area: The formula for the lateral surface area \(A_L\) of a cone is given by: \[ A_L = \pi r l \] where \(l\) is the slant height (hypotenuse given as 22 cm): \[ A_L = 3.14 \times 12.5 \times 22 \] \[ A_L = 3.14 \times 275 = 865.5 \text{ cm}^2 \]
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Total surface area: \[ \text{Total Surface Area} = \text{Base Area} + \text{Lateral Area} \] \[ \text{Total Surface Area} = 490.625 + 865.5 = 1356.125 \text{ cm}^2 \]
Since we are to round to the nearest hundredths, we can conclude: \[ \text{Total Surface Area} \approx 1,354.125 \text{ square centimeters} \]
Thus, the correct answer is: 1,354.125 square centimeters.
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