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Q.

If each edge of a cube is doubled, ____ times will volume increase.

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Detailed Solution

Volume (V) of the cube,

= Side 3

⇒ V = a 3

unit cube………………………… (1)
Now here in the question we got that the edge of the cube is doubled.
So now the new edge of the new cube becomes 2a.
And the new cube volume

with edge doubling is

= 2 a 3 = 8 a 3 ⇒ V 1 = 8 a 3

Now from equation (1) we have,

⇒ V 1 = 8 (V)

Hence, the new volume of the cube when the edge is doubled is eight times the old volume of the cube.
If each edge of a cube is doubled, 8 times will volume increase.

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