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
301.44 square inches
301.44 square inches
62.8 square inches
62.8 square inches
94.2 square inches
94.2 square inches
37.68 square inches
37.68 square inches
Responses
301.44 square inches
301.44 square inches
62.8 square inches
62.8 square inches
94.2 square inches
94.2 square inches
37.68 square inches
37.68 square inches
Answers
GPT 3.5
To find the surface area of the cheese wheel, we need to find the surface area of the top and bottom circles, as well as the surface area of the curved side.
The surface area of a circle is found using the formula A = πr², where A is the area and r is the radius. The diameter of the cheese wheel is 6 inches, so the radius is half of that, which is 3 inches.
The surface area of the top and bottom circles is 2π(3)^2 = 2π(9) = 18π square inches.
The surface area of the curved side is found using the formula A = 2πrh, where A is the area, r is the radius, and h is the height.
The surface area of the curved side is 2π(3)(2) = 12π square inches.
Adding the surface area of the top and bottom circles to the surface area of the curved side, we get 18π + 12π = 30π square inches.
Using approximately 3.14 for pi, we can calculate the total surface area of the cheese wheel as 30π square inches, which is approximately 94.2 square inches.
Therefore, the correct answer is 94.2 square inches.
The surface area of a circle is found using the formula A = πr², where A is the area and r is the radius. The diameter of the cheese wheel is 6 inches, so the radius is half of that, which is 3 inches.
The surface area of the top and bottom circles is 2π(3)^2 = 2π(9) = 18π square inches.
The surface area of the curved side is found using the formula A = 2πrh, where A is the area, r is the radius, and h is the height.
The surface area of the curved side is 2π(3)(2) = 12π square inches.
Adding the surface area of the top and bottom circles to the surface area of the curved side, we get 18π + 12π = 30π square inches.
Using approximately 3.14 for pi, we can calculate the total surface area of the cheese wheel as 30π square inches, which is approximately 94.2 square inches.
Therefore, the correct answer is 94.2 square inches.