Surface area of a cube = 6e².
Volume of a cube = e³.
Original cube:
Let e = 1.
Then Volume = 1³ = 1.
Surface area = 6(1²) = 6.
New cube:
Surface area doubled = 2*6 = 12.
Since 6e² = 12, we get:
e² = 2
e = √2.
Volume = e³ = (√2)³ = (√2)(√2)(√2) = 2√2. This is our target.
Now plug V=1 into the answers to see which yield our target of 2√2.
Only B works:
2√2V = 2√2 * 1 = 2√2.
The correct answer is B.
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