Posted by **chandice** on Thursday, October 22, 2009 at 10:57pm.

The areas of the faces of a rectangular box are 48 m2, 96 m2, and 288 m2.

A second box is cubical and each of its faces has area 16 m2.

Find the ratio of the volume of the first box to the volume of the second box.

- math -
**Reiny**, Thursday, October 22, 2009 at 11:22pm
let the sides of the first box be

a, b , and c m

so

ab = 48 #1

ac = 96 #2

bc = 288 #3

divide #1 by #2 --> b/c = 1/2 or c = 2b

divide #2 by #3 --> a/b = 1/3 or b = 3a

divide #1 by #3 --> a/c = 1/6 or c = 6a

we know ab = 48

a(3a) = 48

3a^2 = 48

a^2 = 16

a = 4

then b = 12

and c = 24

the volume of the first box must be

4x12x24 or 1152 m^3

the second box must have each side as 4 m

so its volume is 4x4x4 = 64 m^3

so the ratio of theri volumes = 1152:64

= 18:1

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