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Standard X

Mathematics

Area of Sector

An open box i...

Question

An open box is constructed by starting with a rectangular sheet of metal 10 cm by 14 cm, and cutting a square of side x cm from each corner. The resulting projections are folded up and the seams welded. The volume of the resulting box is:

140 x - 48 x^{2} + 4 x^{3}

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140 x + 48 x^{2} + 4 x^{3}

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140 x + 24 x^{2} + x^{3}

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140 x - 24 x^{2} + x^{3}

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none of these

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Solution

The correct option is E $140 x - 48 x^{2} + 4 x^{3}$
After box welded,
length = 14-2x
breadth = 10-2x
height = x
Volume = lbh = (14-2x)(10-2x)x = (140-48x+4x $^{2}$ )x
$∴$ Volume = 140x-48x $^{2}$ +4x $^{3}$

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An open box is constructed by starting with a rectangular sheet of metal 10 cm by 14 cm, and cutting a square of side x cm from each corner. The resulting projections are folded up and the seams welded. The volume of the resulting box is:

The correct option is E 140x−48x2+4x3After box welded,length = 14-2xbreadth = 10-2xheight = xVolume = lbh = (14-2x)(10-2x)x = (140-48x+4x2)x∴ Volume = 140x-48x2+4x3

The correct option is E $140 x - 48 x^{2} + 4 x^{3}$
After box welded,
length = 14-2x
breadth = 10-2x
height = x
Volume = lbh = (14-2x)(10-2x)x = (140-48x+4x $^{2}$ )x
$∴$ Volume = 140x-48x $^{2}$ +4x $^{3}$