From a thin piece of cardboard 50 in. x 50 in., square corners are cut out so that the sides can be folded up to make a box. What dimensions will yield a box of maximum volume? What is the maximum volume? Round to the nearest tenth, if necessary.
2007-04-24 16:25:27 · 4 answers · asked by bballchic601 1 in Science & Mathematics ➔ Mathematics
Since you are cutting squares, the sides are of equal length. If you use x for the length of the side of a square. This x is also the height when you fold up the sides.
Then.. the volume is length times width times height
V = (50 - 2x)(50 - 2x)x
To find the maximum volume you can graph the equation and locate the heighest point...
or. ..you can take the first derivative of the function and set the derivate equal to zero to locate critical points. The maximum is a critical point. The second derivative will tell you which x-value you've found is a maximum (the second derivative is negative .. graph is concave down when the critical point is a maximum)
2007-04-24 16:37:23 · answer #1 · answered by suesysgoddess 6 · 1⤊ 0⤋
10in. by 5in. will be the best and biggest volume. Assuming I understood the question correctly.
2007-04-24 16:40:16 · answer #2 · answered by eatercrumb 3 · 0⤊ 1⤋
to make a box, square corners dont work.
2007-04-24 16:30:31 · answer #3 · answered by climberguy12 7 · 0⤊ 1⤋
sorry, bud. math confuses me.
good luck, though.
=]
2007-04-24 16:33:02 · answer #4 · answered by Evelyn 3 · 0⤊ 2⤋