Answer:
Let
x cm. be the side of the square to be cut
l
= (45 ? 2x) cm
b
= (24 ? 2x) cm and h = x cm
Volume (V)
of the box = lbh
V = (45 ?
2x) (24 ? 2x) x
=
4x3 ? 138x3 + 1080 x
=
2 [2x3 ? 69x2 + 540x]
=
12 [x2 ? 23x + 90]
Now
is maximum
when x = 5. Here volume of box will be maximum when side of the s square to be
cut = 5 cm.
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