SOLUTION: the mass of an object varies jointly within its density and its volume. If 156 grams of iron has a volume of 20 cm^3 and a density of 7.8 gm/cm^3, what is the volume of 312 grams o

Question 72964: the mass of an object varies jointly within its density and its volume. If 156 grams of iron has a volume of 20 cm^3 and a density of 7.8 gm/cm^3, what is the volume of 312 grams of iron with the same density?
Answer:(blank)cu.cm.
Found 2 solutions by bucky, stanbon:
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The problem tells you that the mass (in grams) of a object varies directly (jointly)
as the volume in cubic cm and the density in grams per cubic cm. In equation form you can
write this as:
.
M = k*V*D
.
where M is mass, V is volume, D is density and k is a constant of proportionality that we
will figure out from the info they gave you.
.
In this problem we are told that a mass of 156 grams results from a volume of 20 cubic cm
and a density of 7.8 grams per cubic cm. Plug these values into the equation and you get:
.
156 = k*20*7.8
.
When you do the multiplication on the right side you get:
.
156 = 156k
.
Therefore, k is 1 for this situation, and our equation simplifies to just
.
M = V*D
.
Then you are asked that if you had a mass of 312 grams of this material which has the
same 7.8 grams per cubic cm density, what is the volume?
.
Start with the equation:
.
M = V*D
.
and substitute the given values:
.
312 = V*7.8
.
Divide both sides by 7.8 and you find that
.
312/7.8 = V
.
which, after the division on the left side, simplifies to
.
40 = V
.
and the units for volume are cubic cm. So the answer to the problem is that the volume
of the new sample of the material is 40 cubic cm.
.
Hope this helps you to understand the problem a little better. Don't get confused by
the constant of proportionality. It's just in there to make both sides of the equation
equal and when you get to more advanced problems of this type it is likely to be needed. I just
showed you how it would fit in and how you would determine it so that later on you won't be
surprised by it.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
the mass of an object varies jointly within its density and its volume. If 156 grams of iron has a volume of 20 cm^3 and a density of 7.8 gm/cm^3, what is the volume of 312 grams of iron with the same density?
-------------
m = k dv
156 = k*7.8*20
k=156/156
k=1
EQUATION
m = dv
312 = 7.8v
v= 40 cm^3
-------------
Cheers,
Stan H.
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