Q. 44.3( 6 Votes )

Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm respectively are melted and formed into a single cube. Find the edge of the new cube formed.

Answer :

Given,


Edge of the first cube = 6 cm


Volume of the first cube = a3 = (6)3 cm


Edge of the second cube = 8 cm


Volume of the second cube = a3 = (8)3 cm


Edge of the third cube = 10 cm


Volume of the third cube = a3 = (10)3 cm


So,


Volume of the formed cube = Volume of the First + Second + Third Cube


Volume of the formed cube = v1 + v2 + v3
= 63 + 83 + 103
= 216 + 512 + 1000
= 1728
Now volume of new cube = a3= 1728
Edge of new cube = a =
1728
a = 12
Therefore surface area of new cube = 6a2
= 6 × 122
= 6 × 12 × 12
= 864 cm2


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