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)
Responses
94.2 square inches
94.2 square inches
62.8 square inches
62.8 square inches
301.44 square inches
301.44 square inches
37.68 square inches
To find the surface area of the cheese wheel, we need to find the area of the top and bottom circles, as well as the area of the curved surface of the cylinder.
The area of a circle is calculated using the formula A = πr^2, where r is the radius of the circle.
Given that the diameter of the cheese wheel is 6 inches, the radius is half of that, which is 6/2 = 3 inches.
Now we can calculate the areas:
1. The area of the top and bottom circles is A = πr^2 = 3.14 * 3^2 = 3.14 * 9 = 28.26 square inches.
2. The circumference of the circle can be found using the formula C = 2πr, which is C = 2 * 3.14 * 3 = 18.84 inches.
To find the area of the curved surface of the cylinder, we can treat it as a rectangle with width equal to the circumference and height equal to the height of the cheese wheel. The formula for the area of a rectangle is A = length * width.
3. The area of the curved surface is A = 18.84 * 2 = 37.68 square inches.
Finally, to find the total surface area, we add the areas of the top and bottom circles to the area of the curved surface:
Total surface area = 2 * (area of top and bottom circles) + area of curved surface
= 2 * 28.26 + 37.68
= 56.52 + 37.68
= 94.20 square inches.
Therefore, the total surface area of the cheese wheel is 94.20 square inches.
The correct answer is 94.2 square inches.