Question

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Answer 1

Answer: Option 1

Step-by-step explanation:

1. You know the lenght of both rectangular prism, therefore if both are similar, the scale factor is:

$sf=\frac{12cm}{4cm}\\sf=3$

2. Then the scale factor of the volumes is:

$sf_v=3^{3}\\sf_v=27$

3. Now, you must multiply the volume of the smalller rectangular prism by the scale factor obtained, then you obtain the following result:

$V_2=(24cm^{3})(27)=648cm^{3}$

Answer 2

Answer: $648 \text{ cube cm}$

Explanation:

When two solid figures are similar then,

$\text{ The ratio of their volume }= (\text{ ratio of their corresponding edges})^3$

Here Given prism having volume $V_1$ and $V_2$ are similar,

Thus, By the given figure,

$\frac{ V_2}{24}= (\frac{12}{4})^3$

$\frac{ V_2}{24}= (3)^3$

$\frac{ V_2}{24}= 27$

$V_2= 27\times 24=648\text{ cube cm}$

⇒ First Option is correct.