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 base, and \( l \) is the slant height.
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Find the radius \( r \):
- The diameter of the cone is 8 in., so the radius is: \[ r = \frac{8}{2} = 4 \text{ in.} \]
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Use the given slant height \( l \):
- The slant height \( l \) is given as 10 in.
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Calculate the surface area:
- Substitute \( r \) and \( l \) into the surface area formula: \[ \text{Surface Area} = \pi (4^2) + \pi (4)(10) \] \[ = \pi (16) + \pi (40) \] \[ = 16\pi + 40\pi \] \[ = 56\pi \]
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Calculate \( 56\pi \) using \( \pi \approx 3.14 \): \[ 56\pi \approx 56 \times 3.14 = 175.84 \text{ in}^2 \]
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Round to the nearest inch: \[ \approx 176 \text{ in}^2 \]
Therefore, the surface area of the cone is approximately 176 in².
The correct answer is 176 in².