A square piece of tin of side 12 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum ? Also, find this maximum volume.

Question

A square piece of tin of side 12 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum ? Also, find this maximum volume.

Filo · Accepted Answer

let the side of square be xThen remaining dimensions of cuboid for volume islength18−2x, width 18−2x and height xVolume(v)=(18−2x)2xdxdv​=(18−2x)2−2x(18−2x)dxdv​=(18−2x)(18−2x−2x)=(18−2x)(18−4x)Nowdxdv​=0 at x=9,29​Now,dx2d2v​=−4(18−2x)−2(18−4x)at x=29​=4.5dx2d2v​<0∴atx=4.5 that is side of square for which we will get maximum volume

Question Text	A square piece of tin of side $12 c m$ is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum ? Also, find this maximum volume.
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A square piece of tin of side $12 c m$ is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum ? Also, find this maximum volume.

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