Question

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

Answer 1

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