To find the total surface area of the cheese wheel, which is a cylinder, we will calculate the surface area using 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
- \( \pi \) is approximately 3.14
First, we find the radius. The diameter of the cheese wheel is given as 6 inches, so:
\[ r = \frac{\text{diameter}}{2} = \frac{6}{2} = 3 \text{ inches} \]
Now, we can use the height which is given as 2 inches.
Now, we can plug our values into the surface area formula:
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Calculate \( 2\pi r^2 \): \[ 2\pi r^2 = 2 \times 3.14 \times (3)^2 = 2 \times 3.14 \times 9 = 56.52 \text{ square inches} \]
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Calculate \( 2\pi rh \): \[ 2\pi rh = 2 \times 3.14 \times 3 \times 2 = 2 \times 3.14 \times 6 = 37.68 \text{ square inches} \]
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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 94.2 square inches.
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