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# ​ help

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10 help

Apr 27, 2020

#1
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Apr 27, 2020
edited by HELPMEEEEEEEEEEEEE  Apr 27, 2020
#2
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Masses are related by their volumes.

If two solids are similar their volumes are related to their corresponding lengths by their cubes in this way:

If a length of solid A has length "La" and the corresponding length of solid B has length "Lb"

and if the volume of solid A has volume "Va" and the volume of solid B has volume "Vb",

then:  Va / Vb  =  (La)3 / (Lb)3.

Also, for areas (by their squares):  Aa / Ab  =  (La)2 / (Lb)2

Let's use this area relationship to find the lengths and then use these lengths to find the volumes.

Aa / Ab  =  (La)2 / (Lb)2     --->   40.32 / 28  =  (La)2 / (Lb)2​     --->   sqrt(40.32) / sqrt(28)  =  La / Lb

Now, let's use the volume formula     --->     Va / Vb  =  (La)3 / (Lb)3     --->    Va / Vb  =  [ sqrt(40.32) ]3 / [ sqrt(28) ]3

Va  =  [ sqrt(40.32) ]3   =  256.024         Vb  =  [ sqrt(28) ]3  =  148.162

We can now use these values for the volumes to find the mass of A:

mass(A) / mass(B)  =  Va / Vb     --->     mass(A) / 6912  =  256.024  / 148.162

--->     mass(A)  =  11944 grams

Apr 27, 2020
#3
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mathsmat  Apr 27, 2020
#4
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Make sure you're learning from this and not just looking for the answers!!

HELPMEEEEEEEEEEEEE  Apr 27, 2020
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Check the answer given at : https://web2.0calc.com/questions/math-problem_67#r1 where you first asked it.  Don't repeat a question without checking the original!

NB Geno made a slight mistake by inverting the ratio on the RHS.

Alan  Apr 27, 2020
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But if A is smaller then B and they are made from the same material, how is the answer 11943.94?

mathsmat  Apr 27, 2020
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HELPMEEEEEEEEEEEEE  Apr 27, 2020
edited by HELPMEEEEEEEEEEEEE  Apr 29, 2020
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"...So the mass of A is 23 1/3 grams..."

Err, not exactly!   Mass of A =   0.5787037037 * 6912 grams

Alan  Apr 27, 2020
#9
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Calculate the mass of A:  Apr 27, 2020
edited by Omi67  Apr 28, 2020
#10
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Thanks...I knew something was wrong with my calculations... HELPMEEEEEEEEEEEEE  Apr 27, 2020