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.
To calculate the total 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 side.
The formula to calculate the surface area of a circle is: A = πr^2, where A is the area and r is the radius.
The radius of the cheese wheel is half of the diameter, so the radius is 6 inches / 2 = 3 inches.
The surface area of the top and bottom circles is A = π(3)^2 = 28.26 square inches each.
Since there are two circles, the total area of both circles is 28.26 square inches x 2 = 56.52 square inches.
The surface area of the side of the cheese wheel is the circumference of the circle multiplied by the height. The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference.
The circumference of the cheese wheel is C = 2π(3) = 18.84 inches.
Therefore, the surface area of the side is 18.84 inches x 2 inches = 37.68 square inches.
The total surface area of the cheese wheel is the sum of the areas of the top, bottom, and side:
Total surface area = 56.52 square inches + 37.68 square inches = 94.20 square inches.
Therefore, the total surface area of the cheese wheel is 94.20 square inches.