Answer:
Surface area = 6l^2
Volume = l^3
If total surface area increased by 2, then the length increased by [tex]\sqrt{2}[/tex]
Volume then is increased by ([tex]\sqrt{2}[/tex]l)^3 = 2[tex]\sqrt{2}[/tex]l^3
1 :2 [tex]\sqrt{2}[/tex]
Which is not an option in the question so this question clearly has a problem.
First of all It's supposed to be "then" not "than," so I'm not sure who teaches math without even knowing this basic grammar.
Second of all, if the answer is 8:1 the question should be "If each sides of a cube is doubled" not "the lateral surface area." Come to think of it what even is lateral surface area of a cube if all sides of the cube is supposed to be same.
Or, if the answer is 2:1 then, it should be If height lateral surface area of a cube is doubled by doubling the height and without changing the length and width" But, then the the shape would no longer be a cube.
Who even wrote this garbage question what.
