#1**0 **

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**

Guest Sep 16, 2020

#2**+2 **

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

Since mass = density * volume

mass_{A} / mass_{B} = (density_{A} * volume_{A}) / (density_{B} * volume_{B})

density_{A} = density_{B} so we can cancel them out

mass_{A} / mass_{B} = volume_{A} / volume_{B}

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 )

volume_{A} / volume_{B} = ( SA_{A} / SA_{B} )^{3/2}

Now we can replace volume_{A} / volume_{B} with mass_{A} / mass_{B}

mass_{A} / mass_{B} = ( SA_{A} / SA_{B} )^{3/2}

Now let's plug in what we know for values of mass_{B} , SA_{A} , and SA_{B}

mass_{A} / 6912 = ( 28 / 40.32 )^{3/2}

Multiply both sides by 6912 and simplify.

mass_{A} = 6912 * ( 28 / 40.32 )^{3/2}

mass_{A} = 4000 and that is in grams

_

hectictar Sep 17, 2020

#3**+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 \((l_A)^3:(l_B)^3\)

Melody Sep 17, 2020

#4**+1 **

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

**Solid A A = 28 cm ^{2}**

I'm gonna use this formula to calculate **a ^{2} ( and b^{2})**

**2(3√3*a ^{2}/2) + 6a^{2} = 28 a^{2} = 2.5008485 a = 1.581407127**

**V _{(A)} = 3√3/2 * a = 10.27502675 cm^{3} **

**~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~**

**Solid B A = 40.32 cm ^{2}**

**2(3√3*b ^{2}/2) + 6b^{2} = 40.32 b^{2} = 3.601221843 b = 1.897688553**

**V _{(B)} = 3√3/2 * b = 17.75524625 cm^{3}**

**~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~**

**V _{(B) } : 6912 = V_{(A)} : x**

*x *= 4000 grams

jugoslav Sep 18, 2020