Question

If the difference between one sixth of sum of length of all edges of a cube and the longest diagonal of the cube is(4÷2+√3)cm, then volume of cube is ?

Answer 1

Solution :

Let the edge of a cube = a cm

sum of length of all edges = 12a cm

length of longest diagonal = √3a cm

According to the problem given ,

(12a)/6 - √3 a = 4/( 2 + √3 )

=> 2a - √3a = 4/( 2 + √3 )

=> a( 2 - √3 ) = 4/( 2 + √3 )

=> a = 4/[ (2+√3)(2-√3)]

=> a = 4/[ 2² - (√3 )² ]

=> a = 4//( 4 - 3 )

=> a = 4 cm

Therefore ,

Volume of the cube = a³

= ( 4 cm )³

= 64 cm³

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