Question

box a has a volume of 32 cubic meters. box b is similar to box a. to create box b, box as dimensions were tripled. what is the volume of box b? 32 m³ 96 m³ 288 m³ 864 m³

Explanation:

Step1: Recall volume - scale - factor relationship

If the scale - factor of the side - lengths of two similar solids is $k$, the ratio of their volumes is $k^{3}$. Here, $k = 3$ (since the dimensions of Box A are tripled to get Box B).

Step2: Calculate the volume of Box B

Let $V_A$ be the volume of Box A and $V_B$ be the volume of Box B. The formula is $V_B=k^{3}V_A$. Given $V_A = 32\ m^{3}$ and $k = 3$, then $V_B=3^{3}\times32$.
$V_B = 27\times32=864\ m^{3}$

Answer:

$864\ m^{3}$