Tingles wants to sell potato chips in cylindrical containers. So the chips do not fall out the containers will have ends. To be environmentally conscious, the company president wants to make the container entirely out of cardboard. Furthermore, they will choose the cylinder that is made with the least amount of cardboard. Cylinder A has a diameter of 4 inches and a height of 2.5 inches. Cylinder B has a diameter of 2 inches and a height of 10 inches. Which containter will they choose?
Surface area = 2(πr^2) * height
Insert your data and decide.
To determine which container has the least amount of cardboard, we need to calculate the surface area of each cylinder.
To find the surface area of a cylinder, we need to calculate the area of the two circular ends, as well as the area of the curved surface.
For Cylinder A:
- Diameter = 4 inches
- Radius (half of the diameter) = 2 inches
- Height = 2.5 inches
The area of each circular end is calculated using the formula for the area of a circle: πr^2, where π (pi) is approximately 3.14.
- Area of one circular end = π * (2)^2 = 12.56 square inches
- We have two circular ends, so the total area of the ends is 2 * 12.56 = 25.12 square inches
To calculate the area of the curved surface, we need to find the circumference of one circular end and multiply it by the height of the cylinder:
- Circumference of one circular end = 2 * π * 2 = 12.56 inches
- Area of the curved surface = Circumference of one circular end * height = 12.56 * 2.5 = 31.4 square inches
Therefore, the total surface area of Cylinder A = Total area of ends + Area of curved surface = 25.12 + 31.4 = 56.52 square inches.
Now let's calculate the surface area of Cylinder B:
- Diameter = 2 inches
- Radius (half of the diameter) = 1 inch
- Height = 10 inches
The area of each circular end is:
- Area of one circular end = π * (1)^2 = 3.14 square inches
- Total area of the ends = 2 * 3.14 = 6.28 square inches
The area of the curved surface is:
- Circumference of one circular end = 2 * π * 1 = 6.28 inches
- Area of the curved surface = Circumference of one circular end * height = 6.28 * 10 = 62.8 square inches
Therefore, the total surface area of Cylinder B = Total area of ends + Area of curved surface = 6.28 + 62.8 = 69.08 square inches.
Comparing the surface areas, Cylinder A has a surface area of 56.52 square inches, while Cylinder B has a surface area of 69.08 square inches.
Since Cylinder A has the smaller surface area, it would use less cardboard and be the more environmentally conscious choice for Tinglers company.