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)

Question

Responses

301.44 square inches
301.44 square inches

37.68 square inches
37.68 square inches

62.8 square inches
62.8 square inches

94.2 square inches
94.2 square inches

Answer 1

To calculate the total surface area of a cylinder (which is the shape of the cheese wheel), we can use the formula:

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

where:

• \( r \) is the radius of the base,
• \( h \) is the height of the cylinder, and
• \( \pi \) is approximately 3.14.

Given:

• The diameter of the cheese wheel is 6 inches, so the radius \( r = \frac{6}{2} = 3 \) inches.
• The height \( h = 2 \) inches.

Now, substituting the values into the formula:

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

Calculating \( (h + r) \):

\[ h + r = 2 + 3 = 5 \]

Now substituting that back into the formula:

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

Calculating step-by-step:

1. Calculate \( 2 \times 3.14 = 6.28 \).
2. Calculate \( 6.28 \times 3 = 18.84 \).
3. Finally, calculate \( 18.84 \times 5 = 94.2 \).

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

\[ \boxed{94.2} \text{ square inches} \]

So the correct answer is 94.2 square inches.