To find the total surface area of the cheese wheel, we need to calculate the surface area of a cylinder, which includes the lateral surface area and the area of the two circular bases.
The formula for the surface area \( A \) of a cylinder is:
\[ A = 2\pi r h + 2\pi r^2 \]
Where:
- \( r \) is the radius
- \( h \) is the height
Given:
- Diameter = 6 inches, hence the radius \( r = \frac{6}{2} = 3 \) inches
- Height \( h = 2 \) inches
- Using \( \pi = 3.14 \)
Now we can calculate the surface area:
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Lateral surface area: \[ \text{Lateral Area} = 2\pi rh = 2 \times 3.14 \times 3 \times 2 \] \[ = 2 \times 3.14 \times 6 = 37.68 \text{ square inches} \]
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Area of the two circular bases: \[ \text{Area of bases} = 2\pi r^2 = 2 \times 3.14 \times (3^2) \] \[ = 2 \times 3.14 \times 9 = 56.52 \text{ square inches} \]
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Total surface area: \[ \text{Total Surface Area} = \text{Lateral Area} + \text{Area of bases} \] \[ = 37.68 + 56.52 = 94.2 \text{ square inches} \]
Thus, the total surface area of the cheese wheel is 94.2 square inches.
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