Question

if you have a large cube with a surface area of 32 and a smaller cube with the surface area of 18 what would the ratio be for the smaller figure to the larger figure
a)2:5
b)5:6
c)3:4
d)6:7

Answer 1

I think you mean, the ratio of the lengths of the smaller and larger cube.
Recall that the surface area of a cube is given by
SA = 6s^2
where s = length of one side
then we get the length of one side of each cube.
Larger:
32 = 6s^2
16/3 = s^2
s = 4/sqrt(3)

Smaller:
18 = 6s^2
3 = s^2
s = sqrt(3)

Finally, we get the ration of smaller length to larger length:
sqrt(3) / (4/sqrt(3))
sqrt(3)*sqrt(3) / 4
3/4 or 3:4

hope this helps~ :)