To find the total surface area of the cheese wheel, which is in the shape of a cylinder, we will use the formula for the surface area of a cylinder:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
Where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
First, we need to find the radius. The diameter of the cheese wheel is 6 inches, so the radius \( r \) is:
\[ r = \frac{diameter}{2} = \frac{6}{2} = 3 \text{ inches} \]
The height \( h \) of the cheese wheel is given as 2 inches.
Now we can substitute these values into the surface area formula:
- Calculate the area of the top and bottom circles (2πr²):
\[ 2\pi r^2 = 2 \times 3.14 \times (3)^2 = 2 \times 3.14 \times 9 = 56.52 \text{ square inches} \]
- Calculate the area of the curved surface (2πrh):
\[ 2\pi rh = 2 \times 3.14 \times 3 \times 2 = 2 \times 3.14 \times 6 = 37.68 \text{ square inches} \]
- 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:
\[ \boxed{94.2} \text{ square inches} \]