Question

# A box is made from a piece of metal sheet 24cms square by cutting equal small squares from each corner and turning up the edges. If the volume of the box is maximum then the dimensions of the box are

A
16,16,4
B
9, 9, 6
C
8, 8, 8
D
9, 9, 8

Solution

## The correct option is A 16,16,4Let square of a cm edge is removedSo Length$$=$$breath$$=24-2a$$ of box$$height = a$$Volume $$=(24-2a)^2a$$$$\frac {dv}{da}=(24-2a)^2-4(24-2a)a$$$$0=(24-2a_)(24-6a)$$$$a=12, 4$$So Length$$=$$ breath$$=16$$$$height =4$$Applied Mathematics

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