Q. 294.4( 52 Votes )

If the length of each edge of a cube is doubled, how many times does its volume become? How many times does its surface area become?

Answer :

Let us assume a be the length of the edge of the cube

We know that,


Volume of cube = a3


Also,


Total surface area of the cube = 6a2


Now, if the length is doubled, then the new length becomes 2a


Now,


New volume = (2a)3 = 8a3


Also,


New surface area = 6 (2a)2 = 24 a2


Therefore,


The total volume of the cube is increased by the actor of 8 whereas the surface area is increased by the factor of 4.


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