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

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

1 answer

To calculate the surface area of the cheese wheel, which is a cylinder, we use the formula for the surface area of a cylinder:

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

Where:

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

Given:

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

Now, plug \( r \) and \( h \) into the surface area formula:

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

Calculating \( (h + r) \):

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

Now substitute that back into the surface area formula:

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

Calculate:

\[ 2 \times 3.14 = 6.28 \] \[ 6.28 \times 3 = 18.84 \] \[ 18.84 \times 5 = 94.2 \]

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

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

The correct answer is 94.2 square inches.