Is my math correct for scaling something in 3 dimensions?

Question

If object $A$ weighs $10$ grams and is, for example, a $1 m^3$ cube, and object $B$ is of the same density but $2$ meters long in every direction rather than $1$ meter long, that would make it an $8 m^3$ cube. I know this much. But since we're multiplying the volume by $8=2\cdot 2\cdot 2$ would the weight also multiply by $8$ to make it $80$ grams, or would it multiply by $2$ and be $20$ grams? I feel stupid that I even have to ask this, and I'm sure it would be but it feels off and it's been really bugging me.

Answer 1

Note the average, or overall, density of any object is the mass per unit volume, i.e., it can be expressed and calculated as

$$d = \frac{m}{v} \tag{1}\label{eq1A}$$

where $d$ is the average density, $m$ is the object's mass and $v$ is its volume. In your case, the object $B$ has the same density as $A$, but it's volume (i.e., the denominator in \eqref{eq1A}) is increased by a factor of $2^3 = 8$. Thus, to keep $d$ unchanged means $m$ must also increase by a factor of $8$. Since $A$'s mass is $10$ grams, this means the mass of $B$ is $10 \times 8 = 80$ grams.