Answer:2.828
Step-by-step explanation:
Given
Surface area of a cube is increased by a factor of 2
Let the original surface area be A
such that new surface area is 2A
for volume we need to know new radius
[tex]6(a')^2=2\times 6r^2[/tex]
where r'=new radius
r=original radius
[tex]a'=\sqrt{2}a[/tex]
New volume(V')[tex]=(a')^3=(\sqrt{2}a)^3[/tex]
[tex]V'=2\sqrt{2}a^3[/tex]
Original volume[tex]=a^3[/tex]
[tex]\frac{V'}{V}=\frac{2\sqrt{2}a^3}{a^3}[/tex]
[tex]V'=2\sqrt{2}V=2.828V[/tex]
