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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?

 

 Nov 24, 2020
 #1
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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

 

 

cool cool cool

 Nov 24, 2020

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