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a cube has a square hole all the way through it. if the volume of wood used to construct the cube is 3072 mm^3, what are the dimensions of the cube and the hole?

 

 Jul 21, 2017
 #1
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The volume of the solid cube is given by :

 

(4x)^3  =  3072 mm^3   simplify

 

64x^3  =  3072  divide both sides by 64

 

x^3  = 48   take the cube root of both sides

 

x = ∛48 mm =  2∛6 mm

 

So each side of the cube is   just   4x  =   4 ( 2∛6 mm )  =  8 ∛6 mm 

 

And the volume of the square hole is just the dimensions 2x * 2x * 4x  

 

(2x)^2 * 4x  =  16 x^3 =  16 ( ∛48)^3  =  16 * 48  = 768 mm^3 

 

 

cool cool cool

 Jul 21, 2017

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