Answer:
The scale factor is 3 : 1.
Step-by-step explanation:
We know that,
The scale factor of the dilation of a prism is the cube root of the ratio of the volume of resultant prism after dilation and the volume of the given prism,
Here, the volume of prism before dilation = 20 cube unit,
And, the volume of the prism after dilation = 540 cube unit,
Thus, by the above statement,
![\text{The scale factor of dilation}=\sqrt[3]{\frac{540}{20}}](https://tex.z-dn.net/?f=%5Ctext%7BThe%20scale%20factor%20of%20dilation%7D%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B540%7D%7B20%7D%7D)
![=\sqrt[3]{27}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B3%5D%7B27%7D)

Hence, the scale factor is 3 : 1.