Respuesta :

carlosego

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:

[tex]sf=\frac{12cm}{4cm}\\sf=3[/tex]

2. Then the scale factor of the volumes is:

[tex]sf_v=3^{3}\\sf_v=27[/tex]

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

[tex]V_2=(24cm^{3})(27)=648cm^{3}[/tex]


Answer: [tex]648 \text{ cube cm}[/tex]

Explanation:

When two solid figures are similar then,

[tex]\text{ The ratio of their volume }= (\text{ ratio of their corresponding edges})^3[/tex]

Here Given prism having volume [tex]V_1[/tex] and [tex]V_2[/tex] are similar,

Thus, By the given figure,

[tex]\frac{ V_2}{24}= (\frac{12}{4})^3[/tex]

[tex]\frac{ V_2}{24}= (3)^3[/tex]

[tex]\frac{ V_2}{24}= 27[/tex]

[tex]V_2= 27\times 24=648\text{ cube cm}[/tex]

⇒ First Option is correct.


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