Final answer:
The total surface area of the cheese wheel is 94.2 square inches. This includes the areas of the two circular faces and the lateral surface area.
Step-by-step explanation:
To calculate the surface area of a cheese wheel, we need to find the area of the two circular faces and the area of the curved surface that wraps around the cheese. The wheel has a diameter of 6 inches, which means the radius is 3 inches (half the diameter). The height is 2 inches.
The area of one circular face is given by the formula A = πr². Using π = 3.14 and the radius r = 3 inches, the calculation is:
A = 3.14 × (3 inches)² = 3.14 × 9 inches² = 28.26 inches²
Since the cheese wheel has two circular faces, we multiply the area calculated for one circle by 2:
Total area of the two circular faces = 2 × 28.26 inches² = 56.52 inches²
To calculate the area of the curved surface, we use the formula for the circumference of a circle, C = 2πr, then multiply it by the height h of the wheel to get the lateral surface area.
Circumference = 2 × 3.14 × 3 inches = 18.84 inches
Lateral surface area = Circumference × Height = 18.84 inches × 2 inches = 37.68 inches²
The total surface area of the cheese wheel is the sum of the areas of the two circular faces and the lateral surface area.
Total surface area = 56.52 inches² + 37.68 inches² = 94.2 inches²
Therefore, the chef will need 94.2 square inches of pastry to cover the cheese wheel.