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Q.

A box is made from a piece of metal sheet 24 cms 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

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a

16,16,4

b

9, 9, 6

c

8, 8, 8

d

9, 9, 8

answer is A.

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Detailed Solution

$Let square of 'a'cm edge is removed So Length=breath = 24 - 2 a of box Volume = (24 - 2 a)^{2} a$
$\begin{array}{l} \frac{d v}{d a} = (24 - 2 a)^{2} - 4 (24 - 2 a) a \\ 0 = (24 - 2 a) (24 - 6 a) \\ a = 12, 4 So Length = breath = 16 h e i g h t = 4 \end{array}$

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A box is made from a piece of metal sheet 24 cms 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