Answer:
b is the correct option [tex]= \sqrt{30 } - 2\sqrt{5} [/tex]
Step-by-step explanation:
We are given a formula of a side of a cube which uses surface area SA
side, [tex]s = \sqrt{\frac{SA}{6} }[/tex]
We are given two cubes. Lets name them as c1 and c2
Surface are of both cubes are given
Surface area of c1 = 180
Surface area of c2 = 120
We are to find out, how much longer is the side of c1, s1 than the side of c2, s2.
For that purpose we will first find out the sides of these cubes
To find side of c1, put SA = 180 in the above side formula
Side of c1, s1 [tex]= \sqrt{\frac{180}{6} }[/tex]
s1 [tex]= \sqrt{30 }[/tex]
Now lets find out the side of c2 by putting SA = 120 in the side formula
Side of c2, s2 [tex]= \sqrt{\frac{120}{6} }[/tex]
s2 [tex]= \sqrt{20 }[/tex]
s2 = [tex]2\sqrt{5}[/tex]
Now we have two sides s1 and s2, and in order to find how much s1 is longer than s2 we have to subtract s2 from s1
s1 - s2 = [tex]= \sqrt{30 } - 2\sqrt{5} [/tex]
