Asked by Motombo
An open box , no more than 5 cm in height, is to be formed by cutting four identical squares from the corners of a sheet metal 25 cm by 32 cm, and folding up the metal to form sides.The capacity of the box must be 1575 (cm squared). What is the side length of the squares removed?
Answers
Answered by
Scott
x (25 - 2x) (32 - 2x) = 1575
expand the cubic equation
find a solver online (use google)
expand the cubic equation
find a solver online (use google)
Answered by
Reiny
size of side of square to be cut out --- x cm
volume = (25-2x)(32-2x)(x)
= 1575
expanding we get:
4x^3-114x^2 + 800x = 1575
4x^3 - 114x^2 + 800x - 1575 = 0
messy to solve, gave up trying to factor, and used Wolfram:
http://www.wolframalpha.com/input/?i=solve+4x%5E3+-+114x%5E2+%2B+800x+-+1575+%3D+0
got x = 3.5 or x = numbers outside the domain of 0 < x < 5
the size of squares to be removed is 3.5 cm by 3.5 cm
check:
3.5(25-7)(32-7)
= 1575
volume = (25-2x)(32-2x)(x)
= 1575
expanding we get:
4x^3-114x^2 + 800x = 1575
4x^3 - 114x^2 + 800x - 1575 = 0
messy to solve, gave up trying to factor, and used Wolfram:
http://www.wolframalpha.com/input/?i=solve+4x%5E3+-+114x%5E2+%2B+800x+-+1575+%3D+0
got x = 3.5 or x = numbers outside the domain of 0 < x < 5
the size of squares to be removed is 3.5 cm by 3.5 cm
check:
3.5(25-7)(32-7)
= 1575
Answered by
Motombo
Thank you