Respuesta :
The volume of the prism, when it is dilated by a scale factor of 3 changed as 7290 meter cube.
What is dilation of solids?
The dilation of the solids is the change of the size of it with a factor, by which it is bigger or smaller from original shape.
Given information-
The volume of the prism is 270 meter cube.
The scale factor of dilation is 3.
As the volume of the prism is 270. The dilation is done by the scale factor of 3. Thus the change in the shape for three dimensions is,
[tex]\Delta =3^3\\\Delta=27[/tex]
Now the volume of the prism is 270. To find the volume of the dilated prism, multiplied 27 by the volume of given prism. Thus the volume of the dilated prism is,
[tex]V_d=27\times270\\V_d=7290\rm m^3[/tex]
Hence, The volume of the prism, when it is dilated by a scale factor of 3 is 7290 meter cube.
Learn more about the dilation of solids here;
https://brainly.com/question/24760202
