To find the surface area of a circular cone, we use the formula:
\[ \text{Surface Area} = \pi r l + \pi r^2 \]
where:
- \( r \) is the radius of the base of the cone,
- \( l \) is the slant height of the cone.
Given:
- Diameter of the cone = 8 in, so the radius \( r = \frac{8}{2} = 4 \) in.
- Slant height \( l = 10 \) in.
Now, we can calculate the surface area:
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Calculate the lateral surface area (the curved surface area): \[ \pi r l = \pi \cdot 4 \cdot 10 = 40\pi \]
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Calculate the base area: \[ \pi r^2 = \pi \cdot 4^2 = 16\pi \]
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Therefore, the total surface area is: \[ \text{Surface Area} = 40\pi + 16\pi = 56\pi \]
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Now, we will calculate \( 56\pi \): \[ 56\pi \approx 56 \cdot 3.14 \approx 175.84 \]
Rounding \( 175.84 \) gives us approximately \( 176 \) in².
Thus, the surface area of the cone to the nearest inch is 176 in².