To find the total surface area of a cylinder (which is the shape of the cheese wheel), we can use the following formula:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
Where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14.
Given:
- The diameter of the wheel of cheese is 6 inches, so the radius \( r \) is half of that: \[ r = \frac{6}{2} = 3 \text{ inches} \]
- The height \( h \) is 2 inches.
Now, we can plug these values into the formula:
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Calculate the area of the two circular bases: \[ 2\pi r^2 = 2 \times 3.14 \times (3)^2 \] \[ = 2 \times 3.14 \times 9 \] \[ = 2 \times 28.26 \] \[ = 56.52 \text{ square inches} \]
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Calculate the area of the curved surface: \[ 2\pi rh = 2 \times 3.14 \times 3 \times 2 \] \[ = 2 \times 3.14 \times 6 \] \[ = 2 \times 18.84 \] \[ = 37.68 \text{ square inches} \]
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Now, add both areas together to get the total surface area: \[ \text{Total Surface Area} = 56.52 + 37.68 \] \[ = 94.2 \text{ square inches} \]
Thus, the total surface area of the cheese wheel is \( \boxed{94.2} \) square inches.
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