SOLUTION: A box with an open top has a square base and four sides of equal height. The volume of the box is 360 cm3 and the surface area is 276 cm2. What are the dimensions of the box, if w

Algebra ->  Systems-of-equations -> SOLUTION: A box with an open top has a square base and four sides of equal height. The volume of the box is 360 cm3 and the surface area is 276 cm2. What are the dimensions of the box, if w      Log On


   

Question 1061554: A box with an open top has a square base and four sides of equal height. The volume of the box is 360 cm3 and the surface area is 276 cm2. What are the dimensions of the box, if we know that the height is greater than both the width and the length?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A box with an open top has a square base and four sides of equal height.
The volume of the box is 360 cm3 and the surface area is 276 cm2.
What are the dimensions of the box, if we know that the height is greater than both the width and the length?
:
let x = the side of the square base
let h = the height of the box
therefore the volume:
x^2 * h = 360
h = h%2Fx%5E2 use this form for substitution
:
and the surface area
x^2 + 4(x*h) = 276
replace h with 360/x^2
x^2 + 4x*360%2Fx%5E2 = 276
cancel x
x^2 + 4360%2Fx = 276
x^2 + 1440%2Fx - 276 = 0
:
Graph this equation
+graph%28+300%2C+200%2C+-4%2C+10%2C+-50%2C+100%2C+x%5E2%2B%281440%2Fx%29-276%29+
x = 6 cm is the side of the square base
then
h = 360/6^2
h = 10 cm is the height
:
:
confirm this by finding the surface area is 276 sq cm
S.A. = 6^2 +4(6*10))
S.A. = 36 + 240