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
62.8 square inches
62.8 square inches
301.44 square inches
301.44 square inches
37.68 square inches
37.68 square inches
94.2 square inches
To find the surface area of the cheese wheel, we need to calculate the surface area of the circular top and bottom, as well as the curved surface area of the side.
The surface area of the circular top and bottom can be found using the formula for the area of a circle: A = πr^2. Since the diameter of the cheese wheel is 6 inches, the radius is half of that, or 3 inches.
The area of each circular top and bottom is therefore:
A = 3.14 x (3 inches)^2 = 3.14 x 9 square inches = 28.26 square inches.
The curved surface area of the side can be found using the formula for the lateral surface area of a cylinder: A = 2πrh, where r is the radius and h is the height. Since the radius is 3 inches and the height is 2 inches, we have:
A = 2 x 3.14 x 3 inches x 2 inches = 2 x 3.14 x 6 square inches = 37.68 square inches.
To find the total surface area, we add the areas of the top, bottom, and side:
Total surface area = 2 x (28.26 square inches) + 37.68 square inches = 56.52 square inches + 37.68 square inches = 94.2 square inches.
Therefore, the total surface area of the cheese wheel is 94.2 square inches.