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A cube with side $' a'$ has a volume $V .$ If we multiply each side by 2, then its new volume will be equal to

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answer is D.

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Detailed Solution

We are given a cube with side

' a'

and the volume is given by

V .

Also, if we multiply each side of the given cube by 2, then we will get a new volume.
We are aware that the volume of a cube =

a 3,

where

a

is any one side of the cube.
Calculating the volume ratio between the new and original cubes as indicated:

⇒ V 1 V = 2 a 3 a 3 ⇒ V 1 V = 8 a 3 a 3 ⇒ V 1 V = 81 ⇒ V 1 = 8 V

As a result, the volume increases to 8V, or 8 times the initial volume.
Hence, option (4) is correct.

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