Question

question 15 (multiple choice worth 1 points) box a has a volume of 48 cubic meters. box b is similar to box a. to create box b, box as dimensions were doubled. what is the volume of box b? 24 m³ 96 m³ 144 m³ 384 m³

Explanation:

Step1: Recall volume - scale factor relationship

If the linear - scale factor between two similar solids is $k$, the volume - scale factor is $k^{3}$.

Step2: Determine the linear - scale factor

Since the dimensions of Box A are doubled to get Box B, the linear - scale factor $k = 2$.

Step3: Calculate the volume of Box B

The volume of Box A is $V_A=48\ m^{3}$. The volume of Box B, $V_B$, is related to the volume of Box A by the formula $V_B=k^{3}V_A$. Substitute $k = 2$ and $V_A = 48\ m^{3}$ into the formula: $V_B=2^{3}\times48$.
$2^{3}=8$, so $V_B=8\times48 = 384\ m^{3}$.

Answer:

$384\ m^{3}$