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
Answer This Question
Related Questions
 math  The areas of the faces of a rectangular box are 48 m2, 96 m2, and 288 m2...
 Math  The areas of the faces of a rectangle box are 48 m2, 96 m2, and 288 m2. A...
 Math  The areas of the rectangular faces of the box are shown( 90 in.², 60 in...
 Algebra  The surface area of a box is 160. The length of the box is twice its ...
 math  the areas of the rectangular faces are: 90, 54, and 60. What is the ...
 Geometry  Find the volume of a rectangular box. The faces have areas of 15, 25...
 Sixth Grade Math  To find the surface area of a box, add the areas of the faces...
 Maths  Differentiation  A closed rectangular box is made with sides of length...
 math check  please check: this deals with a rectangular prism: RECTANGULAR ...
 algebra 2  The volume of the box is represented by (x^2+5x+6)(x+5). Find the ...
More Related Questions