Question

box a has a volume of 512 cubic meters. box b is similar to box a. to create box b, box as dimensions were divided by 2. what is the volume of box b?

Explanation:

Step1: Recall volume - ratio for similar solids

For similar solids, if the linear - scale factor is $k$, the volume - scale factor is $k^{3}$. Here, the linear dimensions of Box A are divided by 2 to get Box B, so the linear - scale factor $k=\frac{1}{2}$.

Step2: Calculate the volume of Box B

Let the volume of Box A be $V_A = 512$ cubic meters and the volume of Box B be $V_B$. The volume - scale factor relationship is $\frac{V_B}{V_A}=k^{3}$. Substituting $k = \frac{1}{2}$ and $V_A=512$ into the formula, we have $V_B=V_A\times k^{3}$. So $V_B = 512\times(\frac{1}{2})^{3}$.

Step3: Perform the calculation

$(\frac{1}{2})^{3}=\frac{1}{8}$, and $512\times\frac{1}{8}=64$.

Answer:

$64$ cubic meters