Question

a wheel of cheese has a diameter of 6 in and a height of 2 in a shelf is making a appetizer where the cheese will be covered with pastry

Answer 1

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.