Question

The formula s= sa/6 gives the length of the side, s, of a cube with the surface area, sa. How much longer is the side of the cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters ?

Answer 1

`\bf s=\cfrac{sa}{6}\qquad \cfrac{\stackrel{larger}{side}}{\stackrel{smaller}{side}}\implies \cfrac{\quad (180)/(6)\quad }{(120)/(6)}\implies \cfrac{180}{6}\cdot \cfrac{6}{120}\implies \cfrac{180}{120}\implies \cfrac{3}{2}`

they're on a ratio of 3:2, so if the small is 2, the large one is 3, and if the small one is 120, the large one is 180.

on a 3:2 ratio, 3 is larger than 2 by 1 unit, 1 is 50% of 2, or half, so the longer side is 50% larger.

Answer 2

Answer with explanation:

Side of cube = S

Surface Area of Cube = S.A

Relation between Side of a cube and surface area

`S=(S.A)/(6)`

→If surface area of cube =180 Square meters

Side of cube (S)

`S_(1)=(180)/(6)\\\\=30` meters

→ If surface area of cube =120 Square meters

Side of cube (S)

`S_(2)=(120)/(6)\\\\=20` meters

`S_(1)-S_(2)=30 -20=10\\\\S_(1)=S_(2)+10`

Side of cubic having surface area 180 square meters is greater by 10 meters, than a cube with the surface area of 120 square meters.