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

37.68 square inches
37.68 square inches

94.2 square inches
94.2 square inches

62.8 square inches
62.8 square inches

301.44 square inches

Answer 1

To find the total surface area of the cheese wheel, we can use the formula for the surface area of a cylinder, which is given by:

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

where:

• \( r \) is the radius,
• \( h \) is the height,
• \( \pi \) is approximately 3.14.

From the question, we know:

• The diameter of the cheese wheel is 6 inches, so the radius \( r \) is half of that: \[ r = \frac{6}{2} = 3 \text{ inches} \]

• The height \( h \) of the cheese wheel is 2 inches.

Now we can plug in the values into the surface area formula:

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

Calculating the height plus radius: \[ h + r = 2 + 3 = 5 \]

Now plug that back into the surface area 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. Then \( 6.28 \times 3 = 18.84 \)
3. Lastly, \( 18.84 \times 5 = 94.2 \)

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.