SOLUTION: A small square of side length x cm is cut from each corner of a square cardboard of side length 10 cm, then the area of the remaining piece of cardboard is? Ans: (10-2x)(10-2x)

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A small square of side length x cm is cut from each corner of a square cardboard of side length 10 cm, then the area of the remaining piece of cardboard is? Ans: (10-2x)(10-2x)       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 479463: A small square of side length x cm is cut from each corner of a square cardboard of side length 10 cm, then the area of the remaining piece of cardboard is?
Ans: (10-2x)(10-2x) which will give me (10-2x)^2
And the greatest volume? 10-2x* 10-2x * x
And then I expand but I don't know what to do next
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
to continue
(10-2x)^2*x
(100-40x+4x^2)*x= Volume
100x-40x^2+4x^3= Vol
dv = 100-80x+12x^2
You get maximum volume when dv =0
12x^2-80x+100=0
Find the roots of the equation by quadratic formula

a= 12 ,b= -80 ,c= 100
b^2-4ac= 6400 - -4800
b^2-4ac= 1600
sqrt%28%091600%09%29= 40
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 80 + 40 )/ 24
x1= 5
x2=( 80 -40 ) / 24
x2= 1.67
cut off square = 1.67 x 1.67