Answer: [tex]2,160\ ft^3[/tex]
Step-by-step explanation:
The first step is to find the ratio of the lengths.
According to the information given in the exercise, one the solids has edges of 12 feet and the other solid has edges of 24 feet.
Therefore, the ratio of the length of the smaller solid to the length of the is the following:
[tex]k=\frac{24\ ft}{12\ ft}\\\\k=2[/tex]
Now, the ratio to the volumes of the smaller solid to the other one is the following:
[tex]k^3=2^3=8[/tex]
Then, knowing that the volume of the smaller solid is:
[tex]V_s=270\ ft^3[/tex]
You get that the volime of the larger solid is:
[tex]V_l=270\ ft^3*8\\\\V_l=2,160\ ft^3[/tex]
