A factory makes plastic barrels. The barrels have a diameter of 2.25 feet and a height of 3 feet. The plastic used to make them costs $2.60 per square foot. What would be the cost of the plastic to make 10 barrels?

1 Answer
EZ as pi
Feb 12, 2018

#$758.11#

Explanation:

You need to find the surface area of the barrels. This consists of the area of the lid and the bottom, which are both circles, as well as the curved surface which flattens out into a rectangle.

The formula for the surface area of a cylinder closed at both ends:

#TSA = 2pir^2 + 2pirh#

The diameter is #2.25ft#, so the radius is #1.125ft#.
The height is #3ft#.

#TSA = 2pi(1.125)^2 + 2pi(1.125)(3)#

#= 2.53125pi + 6.75pi#

#=9.28125pi#

#= 29.158ft^2#

Find the cost of one barrel at #$2.60# per square foot:

#29.158 xx$2.60 = $75.811#

Therefore you can find the cost of #10# barrels:

#$75.81+10 = $758.11#

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