We want to find the volume of the following truncated pyramid.
To do so, we can first find the volume of the original pyramid, and then subtract from it the volume of the removed top. Let's do it!
Original Volume
We know that the original pyramid had a height of 12 centimeters. We also know that its base is a square, with each side being 9 centimeters long. Let's draw this pyramid.
The volume of a square-based pyramid is the product of its base area and height divided by 3.
V=1/3 B h ⇔ V=1/3 s^2 h
Let's substitute the height and side of the base area in the formula and evaluate.
We know that the volume of the original pyramid is 324 cubic centimeters.
Top's Volume
Now, let's find the volume of the removed top. We know that the slice was made parallel to the base. Because of that, the removed top is a pyramid that is similar to the original one. To find the linear scale factor between the two pyramids, let's divide the base's side of the original pyramid ( 9) by the base's side of the top ( 3).
Linear scale factor = 3/9 = 1/3
The linear scale factor is 13. The volume scale factor is a cube of the linear scale factor.
Linear scale factor = 1/3
⇓
Volume scale factor = ( 1/3)^3 = 1/27
To find the top pyramid's volume, we should multiply the volume of the original pyramid by the volume scale factor. Let's do it!
To find the truncated pyramid's volume, we will subtract the removed top's volume from the original pyramid's volume. Let's do it!
324-12=312
The truncated pyramid has a volume of 312 cubic centimeters.
