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Question
A box without lid having maximum possible volume is to be made from a rectangular piece of tin 32 cm x 20 cms by cutting of equal square pieces from the four corners and turning up the projecting pieces to make the sides of the box. The height of the box is equal to
A box without lid having maximum possible volume is to be made from a rectangular piece of tin 32 cm x 20 cms by cutting of equal square pieces from the four corners and turning up the projecting pieces to make the sides of the box. The height of the box is equal to
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Solution
The correct option is D 4
Let we remove square of edge b cm
So Length=32−2b breath =20−2b height =b
Volume=(32−2b)(20−2b)b
dvdb=(32−2b)(20−2b)+2(2b−20)b+2(2b−32)b
0=4(16−b)(10−b)+4(b)(2b−26)
So b=4
Let we remove square of edge b cm
So Length=32−2b breath =20−2b height =b
Volume=(32−2b)(20−2b)b
dvdb=(32−2b)(20−2b)+2(2b−20)b+2(2b−32)b
0=4(16−b)(10−b)+4(b)(2b−26)
So b=4
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