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)

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) (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
= 40

x1=( 80 + 40 )/ 24
x1= 5
x2=( 80 -40 ) / 24
x2= 1.67
cut off square = 1.67 x 1.67
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