A wheel of cheese has a diameter of 6 in and a height of 2 in 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 find the surface area of the cheese wheel, we need to calculate the surface area of the top and bottom circles (the cheese's ends) and the surface area of the curved side of the cylinder (the cheese's height).
The formula for the surface area of a circle is: A = πr^2, where A is the area and r is the radius.
Given that the diameter of the cheese wheel is 6 inches, the radius (r) is half of that, which is 6 / 2 = 3 inches.
Calculating the surface area of each end (circle):
A_end = πr^2 = 3.14 * 3^2 = 3.14 * 9 = 28.26 square inches
The cheese wheel has two ends, so the total surface area of the ends is 2 * 28.26 = 56.52 square inches.
The height of the cheese wheel is 2 inches, which is the same as the curved side of the cylinder.
To find the surface area of the curved side of the cylinder:
A_side = circumference * height
To calculate the circumference of the cheese wheel, we need the radius (r):
C = 2πr = 2 * 3.14 * 3 = 18.84 inches
Therefore, the surface area of the curved side of the cylinder is:
A_side = 18.84 * 2 = 37.68 square inches.
The total surface area of the cheese wheel is the sum of the surface area of the ends and the surface area of the side:
Total surface area = surface area of ends + surface area of side
Total surface area = 56.52 + 37.68 = 94.20 square inches.
So, the total surface area of the cheese wheel is 94.20 square inches.