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

94.2 square inches

62.8 square inches

301.44 square inches

37.68 square inches

Answer 1

[AI-generated answer — Bot GPT 3.5]

The surface area of the cheese wheel can be calculated by finding the area of the top and bottom circles and the area of the curved side.

The area of the top and bottom circles (which are the same) can be calculated using the formula for the area of a circle: A = πr^2, where r is the radius. The diameter of the cheese wheel is given as 6 inches, so the radius is half of that, which is 6/2 = 3 inches.

A1 = π(3)^2 = π(9) = 28.26 square inches

The area of the curved side can be calculated by finding the circumference of the circle and multiplying it by the height of the wheel. The circumference of a circle is given by the formula: C = 2πr.

C = 2π(3) = 6π = 18.84 inches

A2 = 18.84 inches * 2 inches = 37.68 square inches

To find the total surface area, we add the area of the top and bottom circles to the area of the curved side.

Total surface area = A1 + A2 = 28.26 square inches + 37.68 square inches = 65.94 square inches

Rounding to the nearest tenth, the total surface area of the cheese wheel is 65.9 square inches.

Answer 2

use the answer i provided you, idc if its not right

Answer 3

[AI-generated answer — Bot GPT 3.5]

Sorry for the confusion earlier. If you wish to use the answer you provided, then the total surface area of the cheese wheel would be 94.2 square inches.

Answer 4

[AI-generated answer — Explain Bot]

To find the total surface area of the cheese wheel, we need to calculate the area of the top and bottom circles and the area of the curved part.

1. Let's start by finding the area of one circle on the top or bottom of the cheese wheel.
- The formula for the area of a circle is A = π * r^2, where A is the area and r is the radius.
- The diameter of the cheese wheel is given as 6 inches, so the radius (r) is half of that, which is 3 inches.
- Plugging in the values, the area of one circle is A = 3.14 * (3^2) = 3.14 * 9 = 28.26 square inches.

2. Since there are two circles (top and bottom), we need to multiply this area by 2: 28.26 * 2 = 56.52 square inches.

3. Next, we need to find the area of the curved part.
- The curved part forms a cylinder, so the formula for the lateral surface area of a cylinder is A = 2πrh, where r is the radius and h is the height.
- Plugging in the values, the area of the curved part is A = 2 * 3.14 * 3 * 2 = 37.68 square inches.

4. To find the total surface area, we add the area of the circles and the area of the curved part: 56.52 + 37.68 = 94.2 square inches.

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