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)
I apologize for the mistake.
To calculate the surface area of the cheese wheel, we need to find the area of the two circular bases and the lateral surface area.
The area of each circular base can be calculated using the formula for the area of a circle: A = πr^2.
The radius of the cheese wheel is half the diameter, so it is 6/2 = 3 inches.
The area of each circular base is therefore A = 3.14 * (3^2) = 3.14 * 9 = 28.26 square inches.
The lateral surface area can be calculated using the formula for the surface area of a cylinder: A = 2πrh.
The radius is 3 inches and the height is 2 inches.
So the lateral surface area is A = 2 * 3.14 * 3 * 2 = 37.68 square inches.
To find the total surface area, we add the areas of the two circular bases to the lateral surface area: 28.26 + 28.26 + 37.68 = 94.2 square inches.
Therefore, the total surface area of the cheese wheel is 94.2 square inches. Answer: \boxed{94.2}.
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To find the total surface area of the cheese wheel, we need to calculate the combined area of the curved surface and the top and bottom surfaces.
First, let's find the area of the curved surface. This can be calculated using the formula for the lateral surface area of a cylinder, which is 2πrh, where π represents the value of pi, r is the radius, and h is the height.
Given that the diameter of the cheese wheel is 6 inches, we can calculate the radius (r) by dividing the diameter by 2: r = 6/2 = 3 inches.
Using the given height of 2 inches, we can substitute the values into the formula:
Curved surface area = 2πrh = 2 * 3.14 * 3 * 2 = 37.68 square inches.
Next, let's find the area of the top and bottom surfaces, which are both circles with a radius of 3 inches.
The formula for the area of a circle is given by πr^2.
Area of each circle = πr^2 = 3.14 * (3)^2 = 3.14 * 9 = 28.26 square inches.
Since there are two identical circles (top and bottom surfaces), we multiply the area of one circle by 2.
Area of top and bottom surfaces = 2 * 28.26 = 56.52 square inches.
Finally, we can find the total surface area by adding the curved surface area and the area of the top and bottom surfaces:
Total surface area = Curved surface area + Area of top and bottom surfaces = 37.68 + 56.52 = 94.20 square inches.
Therefore, the total surface area of the cheese wheel is 94.20 square inches.
The radius of the cheese wheel is half the diameter, so it is 6/2=<<6/2=3>>3 inches.
The chef calculates the area of the circular base of the cheese, as 3.14*3^2 = <<3.14*3^2=28.26>>28.26 square inches.
The height of the cheese wheel is 2 inches.
The chef will also need to cover the top of the cheese wheel with pastry, which is another 3.14*3^2 = <<3.14*3^2=28.26>>28.26 square inches.
The total surface area of the cheese wheel is 28.26 + 28.26 + 28.26 = <<28.26+28.26+28.26=84.78>>84.78 square inches. Answer: \boxed{84.78}.