# Math

a soup manufacturer is trying to decide between two containers for packaging soup for sale.

option A- the soup is packaged in a cylindrical can made of steel and tin. The cylinder has a height of 4.25 in. and a radius of 1.625 in. The packaging material costs \$0.00043 per square inch

Option B- The soup is packaged in a container shaped like a rectangular prism and is made of paperboard, plastic, and aluminum foil. The container has a length of 3.5 in., a width of 1.5 in., and a height of 6.7 in. The packaging material costs \$0.00036 per square inch.

Based on the cost of the packaging, which container is cheaper. Showing work is appreciated

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1. Cylinder:
Total area of top and bottom 2 (pi r^2)
Total area of side = 2 pi r h
Total area = 2 pi r (r+h)
Box:
top and bottom area = 2 ( length * width)
sides = 2 * length*height
ends = 2 * width * height
so total area of box = 2 (Lw +Lh +wh)
==============
multiply each by cost/in^2 to compare total costs

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2. the area of a cylinder is 2πr(r+h)
A: 2π*1.625(1.625+4.25) * 0.00043 = \$0.0258

the area of a prism is 2(lw+wh+lh)
B: 2(3.5*1.5 + 1.5*6.7 + 3.5*6.7) * 0.00036 = \$0.0279

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3. PS, no one in their right mind stores soup in a box.

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4. thank you guys for the help

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