To determine how much pastry you would need to cover the wheel of cheese, we can consider the cheese as a cylinder. Given that the diameter is 6 inches, the radius is half of that, which is 3 inches (6 in / 2). The height is 2 inches.
Step 1: Calculate the surface area of the cheese
A cylinder's surface area \( A \) can be calculated using the formula:
\[ A = 2\pi r(h + r) \]
Where:
- \( r \) is the radius,
- \( h \) is the height.
Substituting in the values:
- \( r = 3 \) inches,
- \( h = 2 \) inches.
\[ A = 2\pi(3)(2 + 3) = 2\pi(3)(5) = 30\pi \]
Step 2: Calculate the surface area
Using the value of \( \pi \approx 3.14 \):
\[ A \approx 30 \times 3.14 \approx 94.2 \text{ square inches} \]
Step 3: Prepare the pastry
You will need approximately 94.2 square inches of pastry to fully cover the wheel of cheese. For practical considerations, you may want to have a little extra pastry on hand to account for seams or any mistakes while covering the cheese.
Summary
To cover a cylindrical wheel of cheese with a diameter of 6 inches and a height of 2 inches, you would need approximately 94.2 square inches of pastry.
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