+1982 A new company is starting up and they are creating care packages to be sent to children in high poverty areas. All of the items for the package need to fit inside of one container that does not have a lid. The company has a great team that is designing a container that has a total volume of 2.5 ft^3. For the shape, they are deciding between a rectangular prism with a base dimension of 1 ft x 2 ft and a cylinder with a base area of 2.5 ft^2. The material they have selected to make the packages cost $1.30 per square foot. Which package design will cost the company less to create and by approximately how much? Use π = 3.14
+37146 https://web2.0calc.com/questions/which-package-design-will-cost-the-company-less-to
+129852 We need to find the height of both objects and the radius of the cylinder
For the rectangular prism, we have
2.5 = (base area)(height
2.5 = (2 *1) * height
2.5 = 2 * height divide both sides by 2
1.25 = height
The surface area = base area + side area =
(2* 1) + 2 * (1.25)( 2 + 1) = 2 + 2.5 ( 3) = 9.5 sq ft
So.....the total cost = 9.5 * 1.30 = $12.35
For the cylinder we have that
2.5 = base area * height
2.5 = 2.5 * height divide both sides by 2.5
1 = height
The radius can be found as
2.5 = pi * radius^2
2.5 = 3.14 * radius^2 divide both side by 3.14
2.5 /3.14 = radius^2 take the square root
√[2.5 / 3.14 ] = radius
The total surface area = base area + side area = 2.5 + 2 * pi * radius * height =
2.5 + 2 * 3.14 * √[2.5/3.14) * 1 =
2.5 + 2*3.14√[2.5/3.14]
So....the total cost for the cylinder =
1.30 ( 2.5 + 2* 3.14√[2.5/3.14] ) = $10.54
So....the cylinder is cheaper
