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.(
A.94.2 square inches
B. 62.8 square inches
C. 301.44 square inches
D. 37.68 square inches
To find the surface area of the cheese wheel, we need to find the area of the two circles that make up the top and bottom of the cheese wheel, as well as the area of the curved surface.
The area of a circle is given by the formula A = πr^2, where r is the radius of the circle.
Since the diameter of the cheese wheel is 6 inches, the radius is half of that, which is 6/2 = 3 inches.
Using the formula for the area of a circle, the area of each of the top and bottom circles is A = π(3^2) = π(9) = 28.26 square inches.
Next, we need to calculate the area of the curved surface. The curved surface can be thought of as a rectangle that has been rolled into a cylinder, where the height of the rectangle is the same as the height of the cylinder.
The circumference of the cheese wheel is given by the formula C = 2πr = 2π(3) = 6π inches. This is the width of the rectangle.
The height of the rectangle (and the cylinder) is given as 2 inches.
Using the formula for the area of a rectangle, the area of the curved surface is A = 6π(2) = 12π square inches.
Adding up the areas of the two circles and the curved surface, we get a total surface area of 28.26 + 28.26 + 12π square inches.
Using the approximation 3.14 for π, the total surface area is approximately 28.26 + 28.26 + 12(3.14) = 28.26 + 28.26 + 37.68 = 94.2 square inches.
The correct answer is A. 94.2 square inches.