A right square pyramid with base edges of length 8sqrt2 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?
+128448 The length of the diagonal on the base of the pyramid = 8sqrt (2) * sqrt (2) =16
Hafl of this length = 8
Height of the pyramild = sqrt (10^2 - 8^2 ) = sqrt 36 = 6
Then the height of the smaller pyramid = 6 - 4 = 2
These pyramids are similar so the scale factor is 2/6 = 1/3
Volume of the larger pyramid = (1/3) side^2 * height = (1/3) (8sqrt (2) )^2 * 6 = 2 * 128= 256 units^3
Volume of smaller pyramid = volume of large pyramid * scale factor ^3 = 256 (1/3)^3 = 256/8 = 32 units^3
