SOLUTION: The density of steel is approximately 7.8 grams per cubic centimeter. An empty steel can with a mass of 76 grams has a radius of 6.1 centimeters and a height of 6.3 centimeters. Es

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The density of steel is approximately 7.8 grams per cubic centimeter. An empty steel can with a mass of 76 grams has a radius of 6.1 centimeters and a height of 6.3 centimeters. Es      Log On

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Question 1201628: The density of steel is approximately 7.8 grams per cubic centimeter. An empty steel can with a mass of 76 grams has a radius of 6.1 centimeters and a height of 6.3 centimeters. Estimate the thickness of the steel. Round your answer to the nearest hundredth.
Answer by ikleyn(52835) About Me  (Show Source):
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The density of steel is approximately 7.8 grams per cubic centimeter.
An empty steel can with a mass of 76 grams has a radius of 6.1 centimeters
and a height of 6.3 centimeters.
Estimate the thickness of the steel. Round your answer to the nearest hundredth.
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To estimate the thickness of the steel in this problem, it is ENOUGH to calculate 
the surface area, S, of the can.


Then you will write this equation for the mass 

        S*t*d = 76 grams,    (1)

where t is the thickness (which is small and is assumed uniform over the entire surface),
d is the steel density.


This equation contains only one unknown t, which is under the problem's question
and which you will find from equation (1) as 

        t = 76%2F%28S%2A7.8%29.    (2)


So, the only thing to work on is to find the surface area of the can.


The radius is 6.1 cm, the height is h= 6.3 cm, pi = 3.14 (approximately), so the surface area is

    S = 2%2Api%2Ar%5E2 + 2pi%2Ar%2Ah = 2%2A3.14%2A6.1%5E2+%2B+2%2A3.14%2A6.1%2A6.3 = 475.0192 cm^2,

which you can round to 475 cm^2.


Now the thickness of the material (steel) is, according formula (2)

    t = 76%2F%28475%2A7.8%29 = 0.0205 centimeters,


or, in more appropriate units, 0.2 millimeters.   ANSWER

Solved.

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This problem teaches you to apply common sense, along with the school geometry basics.