Answer:
So, first let's understand what a scale factor is. A scale factor is a number that tells you how much you need to multiply the size of an object to make it bigger or smaller. In this case, the scale factor is 1/3, which means we're going to make the pyramid one third of its original size.
Now, let's talk about how we can find the volume of the pyramid. The formula for the volume of a pyramid is:
Volume = (1/3) x base area x height
The base area is the area of the rectangle at the bottom of the pyramid, which we can find by multiplying the length and width:
Base area = 9 cm x 12 cm = 108 square cm
The height of the pyramid is given as 15 cm, so we can substitute these values into the formula:
Volume = (1/3) x 108 square cm x 15 cm
Volume = 540 cubic cm
So the volume of the original pyramid is 540 cubic cm. But we need to find the volume of the pyramid after it is dilated by a scale factor of 1/3. To do this, we need to multiply the original volume by the scale factor cubed. The reason we cube the scale factor is because we're scaling in three dimensions (length, width, and height).
Scale factor cubed = (1/3) x (1/3) x (1/3) = 1/27
Volume of dilated pyramid = 540 cubic cm x 1/27
Volume of dilated pyramid = 20 cubic cm (rounded to the nearest whole number)
So the volume of the pyramid after it is dilated by a scale factor of 1/3 is 20 cubic cm.