SOLUTION: Please help me solve this equation: A rectangular box that is closed at the top is constructed so that its length, width, and height are in the ratio 5 : 4 : 2, respectively. If t
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Question 621199: Please help me solve this equation: A rectangular box that is closed at the top is constructed so that its length, width, and height are in the ratio 5 : 4 : 2, respectively. If the surface area of the box is 931 square centimeters, what is the number of cubic centimeters in the volume of the box? Thanks Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A rectangular box that is closed at the top is constructed so that its length, width, and height are in the ratio 5 : 4 : 2, respectively.
If the surface area of the box is 931 square centimeters, what is the number of cubic centimeters in the volume of the box?
:
Let x = the multiplier
then
5x = the length
4x = the width
2x = the height
:
Surface area formula: S.A. = 2(L*W)+2(L*H)+2(W*H)
therefore
2(5x*4x) + 2(5x*2x) + 2(4x*2x) = 931
2(20x^2) + 2(10x^2) + 2(8x^2) = 931
40x^2 + 20x^2 + 16x^2 = 931
76x^2 = 931
x^2 = 931/76
x^2 = 12.25
x =
x = 3.5 is the multiplier
hence
5*3.5 = 17.5 is the length
4*3.5 = 14.0 is the width
2*3.5 = 7.0 is the height
:
Find the volume
V = 17.5 * 14 * 7
V = 1715 cu/cm is the volume
