Question

if a cube has surface area S and volume V then the volume of the cube of surface area 2S is ?​

Answer 1

Let the side of cube be a.

a³ = V

And,

6a²= S----(i)

Now,

If surface area is 2S, then

2S = 6a²

=> 2S = 12a²

=> S = 6a²

So,

a = under root S/6

Volume = a³

= S/6× √ S/6

Answer 2

given the surface area of cube = S

and volume of the cube = V

formula to find the surface area of a cube is 6a²

so we can write,

➡ 6a² = S (a is the side of the cube)

now, we have to find the volume of the cube when surface area is 2S

➡ 6a² = 2S

➡ a² = 2S/6

➡ a² = S/3

➡ a = √(S/3)

therefore it's volume = a³

= [√(S/3)]³

= (√S × √S × √S)/(√3 × √3 × √3)

= S√S/3√3 cm³