Surface Area of Cylinders Quick Check

Question

5 of 55 of 5 Items

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

37.68 square inches
37.68 square inches

301.44 square inches
301.44 square inches

94.2 square inches
94.2 square inches

62.8 square inches
62.8 square inches

Answer 1

To find the total surface area of a cylinder (in this case, the cheese wheel), you can use the formula:

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

where:

• \( r \) is the radius 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 half of that: \[ r = \frac{6}{2} = 3 \text{ inches} \]
• The height \( h \) is 2 inches.

Now, we can plug the values into the formula:

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

Calculating the terms inside the parentheses first:

\[ 2 + 3 = 5 \]

Now plug everything back into the formula:

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

Calculating step by step:

1. \( 3.14 \cdot 3 = 9.42 \)
2. \( 9.42 \cdot 5 = 47.1 \)
3. \( 2 \cdot 47.1 = 94.2 \)

Thus, the total surface area of the cheese wheel is 94.2 square inches.

The answer is:

94.2 square inches.