Respuesta :
You can use the fact that you can think of the solid as made up of 12 cubes with side length of 1 unit.
The volume of the image of the dilated solid is for k = 1/4 is
3/16 cubic units
How can we interpret measurement of something?
Remember that volume, area, length etc all are measured relatively.
If you are 1.7 meters tall, then you're height is measured relative to meters. This is called unit of the measurement. It means that if we collect 1 meter and 0.7 meters too,they together will be equally tall as you.
Similarly, if we say that a triangle has area of 40 square inches, then it means that its area is equal to 40 squares of 1 inch sides.
Using above understanding to find the volume of the dilated solid
Since the original solid was of 12 cubic units. it means its volume was equal to the total volume of 12 cubes with 1 unit side length.
Now since the scale factor of the dilation is k, that means each of the cube got its side length multiplied by k
Now volume of 12 cubes with side length k units is given by
[tex]V = 12 \times k^3[/tex]
Since it is given that k = 1/4, we have:
[tex]V = 12 \times (\dfrac{1}{4})^3 = \dfrac{3}{16} \: \rm unit^3[/tex] now there are 3/16 cubes with 1 unit length.
Thus,
The volume of the image of the dilated solid is for k = 1/4 is
3/16 cubic units
Learn more about dilated volume here:
https://brainly.com/question/2919998
