The surface area of a cube is 400 millimeters what is the surface area of a similar cube that is larger by a scale factor of 3

Larger by 3 means that the legnths of the sides are larger by 3 times

so we have a cube that has area of 400

surface area=legnth times width times 6 since it is a cube and legnth=width

so

SA=w^2 times 6

6w^2=400

divide by 6

w^2=200/3

square root both sides

w=√ (200/3)

so w is 3 times larger

(3w) ^2 times 6 is new area

w=√ (200/3)

(3√ (200/3)) ^2 times 6=9 (200/3) times 6=600 times 6=3600

answer is 3600 ml^2