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 = a^{3}

Also,

Total surface area of the cube = 6a^{2}

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

Now,

New volume = (2a)^{3} = 8a^{3}

Also,

New surface area = 6 (2a)^{2} = 24 a^{2}

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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