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
94.2 square inches
94.2 square inches
62.8 square inches
62.8 square inches
37.68 square inches
37.68 square inches
To find the surface area of the cheese wheel, we need to calculate the area of the curved surface (the side) and the area of the top and bottom surfaces (the circles).
The area of the curved surface can be found using the formula for the lateral surface area of a cylinder, which is given by 2πrh, where r is the radius and h is the height. Since the diameter of the cheese wheel is 6 inches and the height is 2 inches, the radius is half of the diameter, which is 6/2 = 3 inches. So the area of the curved surface is 2π(3)(2) = 12π square inches.
The area of each of the top and bottom surfaces (the circles) can be found using the formula for the area of a circle, which is given by πr^2, where r is the radius. Again, the radius is 3 inches, so the area of each circle is π(3^2) = 9π square inches.
To find the total surface area, we add the area of the curved surface to the area of the top and bottom surfaces. So the total surface area is 12π + 2(9π) = 12π + 18π = 30π square inches.
Since we are given to use 3.14 for pi, we can approximate the total surface area as 30(3.14) = 94.2 square inches.
Therefore, the correct answer is 94.2 square inches.