A right square pyramid with base edges of length 8*sqrt(2) units each and slant edges of length 10 units each is cut by a plane that is parallel to its base and 4 units above its base. What is the volume, in cubic units, of the new pyramid that is cut off by this plane?
+128475 We can find the height of the larger pyramid as follows
The diagonal distance across the bottom of the base = 8sqrt (2) *sqrt (2) = 16
The height of the larger pyramid = sqrt [ 10^2 - (16/2)^2) = sqrt [ 100 - 8^2] = sqrt [ 100 - 64] = sqrt (36) = 6
The volume of this larger pyramid = (1/3) base area * height= (1/3) (8sqrt 2)^2 * 6 =
(1/3) (128) * 6 = 256 units^3
If the base of the smaller pyramid is 4 units above the base of the larger.....then its height = 6 - 4 = 2
So since these pyramids are similar, the scale factor of the smaller pyramid to the larger = 2/6 = 1/3
So.....the volume of the smaller pyramid = Volume of larger pyramid * (scale factor)^3 =
256 ( 1/3)^3 =
256 / 27 units^3 ≈ 9.48 units^3
