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)%0D%0AResponses%0D%0A%0D%0A301.44 square inches %0D%0A301.44 square inches %0D%0A%0D%0A62.8 square inches%0D%0A62.8 square inches%0D%0A%0D%0A94.2 square inches%0D%0A94.2 square inches%0D%0A%0D%0A37.68 square inches
To calculate the total surface area of the cheese wheel, we need to find the surface area of the base (which is a circle) and the surface area of the side (which is a cylindrical shape).
Surface area of the base (circle):
The diameter of the cheese wheel is 6 inches, so the radius is 6/2 = 3 inches.
The formula for the area of a circle is A = πr^2, where π is approximately 3.14 and r is the radius.
So, the surface area of the base is A = 3.14 * (3 inches)^2 = 3.14 * 9 square inches = 28.26 square inches.
Surface area of the side (cylindrical shape):
The height of the cheese wheel is 2 inches, and the circumference of the cheese wheel can be found using the formula C = πd, where d is the diameter.
So, the circumference of the cheese wheel is C = 3.14 * 6 inches = 18.84 inches.
The formula for the surface area of a cylinder is A = 2πrh, where r is the radius and h is the height.
So, the surface area of the side is A = 2 * 3.14 * 3 inches * 2 inches = 37.68 square inches.
Total surface area of the cheese wheel:
To find the total surface area, we need to add the surface area of the base and the surface area of the side.
Total surface area = surface area of the base + surface area of the side
Total surface area = 28.26 square inches + 37.68 square inches = 65.94 square inches.
Therefore, the total surface area of the cheese wheel is 65.94 square inches.