Posted by **ana** on Thursday, May 17, 2012 at 12:55am.

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

- math -
**Jai**, Thursday, May 17, 2012 at 6:05am
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~ :)

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