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Question 193649: A closed rectangular box has a surface area of 1000 square cm. Its length is twice its width, and its height is six times its width. What is its volume?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A closed rectangular box has a surface area of 1000 square cm.
Its length is twice its width, and its height is six times its width.
What is its volume?
:
Let x = the width
:
"Its length is twice its width,"
L = 2x
:
"its height is six times its width."
h = 6x
:
Surface area equation:
2LW + 2LH + 2WH = 1000
:
simplify, divide equation by 2, results:
LW + LH + WH = 500
:
Substitute x for W, 2x for L, and 6x for H
(2x*x) + (2x*6x) + (x*6x) = 500
:
2x^2 + 12x^2 + 6x^2 = 500
:
20x^2 = 500
:
Divide both sides by 20
x^2 = 25
x = 5 cm is the width
then
2(5) = 10 cm is the length
and
6(5) = 30 cm is the height
;
Vol = 10*5*30 = 1500 cu/cm
:
:
Check solution by finding the surface area:
SA = 2LW + 2LH + 2WH
SA = 2(10*5) + 2(10*30) + 2(5*30)
SA = 2(50) + 2(300) + 2(150)
SA = 100 + 600 + 300
SA = 1000
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