To find the total surface area of a cylinder (the shape of the cheese wheel), we can use the formula:
\[ \text{Surface Area} = 2\pi r(h + r) \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder,
- \( \pi \) is a constant (approximately 3.14 in this case).
For a cheese wheel with a diameter of 6 inches:
- The radius \( r \) is half of the diameter: \[ r = \frac{6}{2} = 3 \text{ inches} \]
Given the height \( h = 2 \) inches, we can substitute \( r \) and \( h \) into the surface area formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 3 \times (2 + 3) \]
Calculating the terms inside the parentheses first:
\[ h + r = 2 + 3 = 5 \]
Now we can plug this back into the formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 3 \times 5 \]
Calculating:
\[ = 2 \times 3.14 = 6.28 \] \[ 6.28 \times 3 = 18.84 \] \[ 18.84 \times 5 = 94.2 \]
Thus, the total surface area of the cheese wheel is:
\[ \text{Surface Area} = 94.2 \text{ square inches} \]
Therefore, the correct answer is 94.2 square inches.
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