Question

A wheel of cheese has a diameter of 6 inches and a height of 2 inch. A chef is making an appetizer where the cheese will be covered with pastry. To know how much pastry is needed, the chef wants to know the surface area of the cheese wheel. What is the total surface area of the cheese wheel in square inches? Use 3.14 for pi.(1 point) Responses 62.8 square inches 62.8 square inches 301.44 square inches 301.44 square inches 94.2 square inches 94.2 square inches 37.68 square inches

Answer 1

To find the total surface area of a cylindrical object (like a cheese wheel), we use the formula for the surface area of a cylinder:

\[
\text{Surface Area} = 2\pi r(h + r)
\]

where \( r \) is the radius and \( h \) is the height.

Given:
- Diameter of the cheese wheel = 6 inches, which gives us a radius \( r = \frac{6}{2} = 3 \) inches.
- Height \( h = 2 \) inches.

Now, we can substitute these values into the formula:

\[
\text{Surface Area} = 2 \times 3.14 \times 3(2 + 3)
\]

First, calculate \( h + r \):
\[
h + r = 2 + 3 = 5
\]

Now, substitute back into the surface area formula:

\[
\text{Surface Area} = 2 \times 3.14 \times 3 \times 5
\]

Calculating:

1. \( 2 \times 3.14 = 6.28 \)
2. \( 6.28 \times 3 = 18.84 \)
3. \( 18.84 \times 5 = 94.2 \)

Thus, the total surface area of the cheese wheel is:

\[
\text{Surface Area} = 94.2 \text{ square inches}
\]

The correct response is **94.2 square inches**.