Three metal cubes whose edges measure 3cm, 4cm and Scm respectively are melted to form a single cube, find its :

  1. 15 cm
  2. 12 cm
  3. 6 cm
  4. none of these
Anurag Mishra Professor Asked on 26th January 2016 in Maths.
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1 Answer(s)

Answer: (3) 6 cm 

Explanation:-
The edge of first cube = 3 cm 
Then, volume of first cube (V1 ) =  3^3 = 3 x 3 x 3 
 = 27 cm^3

The of second cube = 4 cm 
Then, volume of second cube(V2) = 4^3  = 4 x 4 x 4 
 = 64 cm^3

The edge of third cube = 5 cm 
Then, volume of third cube(V3) = 5^3 = 5 x 5 x 5
 = 125 cm^3

After melting, volume of the ‘single’ new cube is V cm3.

Let the edge of the new cube be x cm.

The sum of the volume of the three cubes before melting  = Volume of the new cube formed after melting

V1 + V2 + V3  = V
 27 + 64 + 125  = (x)3   
x3 = 216      x  = 3  = 6 cm

The required edge (of the new cube) is 6 cm.

Hence, the correct answer is option  (3) 6 cm 

Anurag Mishra Professor Answered on 26th January 2016.
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