Question

from a square sheet of cardboard with sides 12units is made a toples box of maximum volume by cutting equal squares at the centers and removing them and turning up the sides. prove that the length of the sides of square is 2units​

Answer 1

Answer:

Answer :

2 cm, 128cm3

Solution :

Let the length cut off from each corner be x cm. Then, length of the box =(12−2x)cm = breadth and height = x cm.

∴V=(12−2x)2×x⇒V=4x3−48x2+144x

∴dVdx=12(x−6)(x−2)andd2Vdx2=24(x−4)

Then, dVdx=0⇒x=2[∵x=6 is not possible]

Also at x=2,d2Vdx2<0

∴V is maximum when x = 2 and maximum V=[(12−4)2×2]cm3