Question 1201628
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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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<pre>
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/(S*7.8)}}}.    (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*pi*r^2}}} + {{{2pi*r*h}}} = {{{2*3.14*6.1^2 + 2*3.14*6.1*6.3}}} = 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/(475*7.8)}}} = 0.0205 centimeters,


or, in more appropriate units, 0.2 millimeters.   <U>ANSWER</U>
</pre>

Solved.


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