A box with no top is to be constructed from a piece of cardboard whose length measures 88 in. more than its width. the box is to be formed by cutting squares that measure 33 in. on each side from the four corners and then folding up the sides. if the volume of the box will be 144144 in. cubed3 , what are the dimensions of the piece of cardboard?

Question

Alfred Butler

Mathematics

3 September, 08:01

A box with no top is to be constructed from a piece of cardboard whose length measures 88 in. more than its width. the box is to be formed by cutting squares that measure 33 in. on each side from the four corners and then folding up the sides. if the volume of the box will be 144144 in. cubed3 , what are the dimensions of the piece of cardboard?

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Answers (1)

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Skye Noble · Answer 1

Let x be the width of the cardboard (which means the length of the cardboard is x+88), then the dimensions of the box are:

Length = [ (x + 88) - 2 (33) ]

Width = x - 2 (33)

Heighth = 33

Volume = length · width · heighth

144,144 = [ (x + 88) - 2 (33) ] · [x - 2 (33) ] · 33

144,144 = (x+22) (x-66) (33)

4368 = (x+22) (x-66)

4368 = x² - 44x - 1452

0 = x² - 44x - 5820

use the quadratic formula to calculate that x = 101

Answer: cardboard width = 101, cardboard length = 189