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# Which package design will cost the company less to create and by approximately how much?

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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

Apr 4, 2019

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https://web2.0calc.com/questions/which-package-design-will-cost-the-company-less-to

Apr 4, 2019
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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 = 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   Apr 4, 2019