Answer: The scale factor is 0.125.
Step-by-step explanation:
Given: The volume of the prism=[tex]360\ yd^3[/tex]
The scaled volume of the prism=[tex]45\ yd^3[/tex]
We know that when we scaled a shape by a scale factor k, then we multiply k to the dimension of the original shape.
So, to find the scale factor k, we need to the divide the scaled volume by the volume of prism , we get
[tex]k=\frac{\text{scaled volume of the prism}}{\text{volume of the prism}}=\frac{45}{360}=\frac{1}{8}=0.125[/tex]
Hence, the scale factor k = 0.125
