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Just cannot seem to get the answer

 Sep 16, 2020
 #1
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Since the 2 solids are similar and made from the same material, then their masses should be proportional to their surface areas: 

 

[28 cm^2 / 40.32 cm^2] x 6,912 =4,800 grams - the mass of A

 Sep 16, 2020
 #2
avatar+9015 
+2

We are given that the solids are made from the same material, which means they have the same density.

 

Since   mass   =   density * volume

 

massA / massB   =   (densityA * volumeA) / (densityB * volumeB)

                                                                                                           densityA = densityB   so we can cancel them out

massA / massB   =   volumeA / volumeB

 

So here we have shown that the ratio of the masses is equal to the ratio of their volumes.

 

Now we need to be careful and remember that the ratio of their volumes is not equal to the ratio of their surface areas.

 

The ratio of their volumes is equal to the ratio of their surface areas raised to the power of 3/2

 

(See https://www.onlinemathlearning.com/similarity-area-volume.html )

 

volumeA  / volumeB   =   ( SAA / SAB )3/2

                                                                    Now we can replace   volumeA / volumeB   with   massA / massB

massA  / massB   =   ( SAA / SAB )3/2

                                                                    Now let's plug in what we know for values of  massB ,  SAA ,  and  SAB

massA / 6912   =   ( 28 / 40.32 )3/2

                                                                    Multiply both sides by  6912  and simplify.

massA   =   6912 * ( 28 / 40.32 )3/2

 

massA   =   4000            and that is in grams

_

 Sep 17, 2020
 #3
avatar+110758 
+2

Thanks Hectictar  

 

With any two similar objects A and B 

 

If a pair of corresponding sides are in the ratio     \(l_A:l_B\)

then

Pairs of corresponding Surface areas will be in the ratio     \((l_A)^2:(l_B)^2\)

 

And for 3 dimensional objects the volumes will be in the ratio        \((l_A)^3:(l_B)^3\)   

 Sep 17, 2020
 #4
avatar+179 
+1

Let a side of a hexagon be equal to the height (or length) of a solid.

 

Solid A          A = 28 cm2

 

I'm gonna use this formula to calculate a2 ( and b2)

 

2(3√3*a2/2) + 6a2 = 28         a2 = 2.5008485          a = 1.581407127

 

V(A) = 3√3/2 * a = 10.27502675 cm3 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solid B          A = 40.32 cm2

 

2(3√3*b2/2) + 6b2 = 40.32         b2 = 3.601221843         b = 1.897688553

 

V(B) = 3√3/2 * b = 17.75524625 cm3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

V(B)  :  6912  =  V(A)  :  x

 

= 4000 grams  smiley

 Sep 18, 2020

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