To find the surface area of a cone, you can use the formula:
\[ \text{Surface Area} = \pi r^2 + \pi r l \]
where \( r \) is the radius of the cone, and \( l \) is the slant height.
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Calculate the radius (r): Since the diameter is 25 cm:
\[ r = \frac{diameter}{2} = \frac{25}{2} = 12.5 , \text{cm} \]
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Calculate the slant height (l): The slant height can be found using the Pythagorean theorem:
\[ l = \sqrt{r^2 + h^2} \]
where \( h \) is the height of the cone (22 cm).
\[ l = \sqrt{(12.5)^2 + (22)^2} = \sqrt{156.25 + 484} = \sqrt{640.25} \approx 25.3 , \text{cm} \]
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Calculate the surface area:
Now, substitute the values for \( r \) and \( l \) into the surface area formula:
\[ \text{Surface Area} = \pi (12.5)^2 + \pi (12.5)(25.3) \] \[ = \pi (156.25) + \pi (316.25) = \pi (156.25 + 316.25) = \pi (472.5) \] \[ \approx 3.14 \times 472.5 \approx 1487.65 , \text{cm}^2 \]
So, the surface area of the cone is approximately 1487.65 cm².