To find the total surface area of a cylinder (which is the shape of the cheese wheel), we need to calculate both the lateral surface area and the area of the two circular bases.
The formula for the total surface area \( A \) of a cylinder is given by:
\[ A = 2\pi r h + 2\pi r^2 \]
where:
- \( r \) is the radius,
- \( h \) is the height.
Given the diameter of the cheese is 6 inches, the radius \( r \) is:
\[ r = \frac{diameter}{2} = \frac{6}{2} = 3 \text{ inches} \]
The height \( h \) is given as 2 inches.
Now we can plug these values into the formula:
- Calculate the lateral surface area:
\[ \text{Lateral Surface Area} = 2\pi r h = 2 \times 3.14 \times 3 \times 2 \]
Calculating this:
\[ = 2 \times 3.14 \times 3 \times 2 = 2 \times 3.14 \times 6 = 37.68 \text{ square inches} \]
- Calculate the area of the two circular bases:
\[ \text{Area of one base} = \pi r^2 = 3.14 \times (3)^2 \]
Calculating this:
\[ = 3.14 \times 9 = 28.26 \text{ square inches} \]
Since there are two bases:
\[ \text{Total Base Area} = 2 \times 28.26 = 56.52 \text{ square inches} \]
- Now add the lateral surface area and the total base area to get the total surface area:
\[ A = \text{Lateral Surface Area} + \text{Total Base Area} \]
\[ A = 37.68 + 56.52 = 94.20 \text{ square inches} \]
Therefore, the total surface area of the cheese wheel is 94.20 square inches.