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tiwaribianca475
31.07.2019 •
Mathematics
Abox with no top is to be constructed from a piece of cardboard whose length measures 12 inches more than its width. the box is formed by cutting squares that measure 4 inch on each side from the four corners and then folding up the sides. if the volume of the box 256 in cm^3 what are the dimensions of the piece of cardboard? the height? the width?
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Ответ:
Width is 12 inches and height is 4 inches.
Step-by-step explanation:
Let the width of the piece of cardboard be = w inches
Then length is =
inches
As given, 4 inch squares are cut from each corner;
So, the width is =
inches
Length is =
inches
When we are folding the cut portion, that gives the height as = 4 inches
The volume is given by : length x width x height
And volume is given as 256 cubic inches
So,![256=(w+4)(w-8)(4)](/tpl/images/0155/2674/f90c4.png)
=>![256=(w^{2}-4w-32)4](/tpl/images/0155/2674/9ffe5.png)
=>![64=(w^{2}-4w-32)](/tpl/images/0155/2674/732f9.png)
=>![w^{2} -4w=96](/tpl/images/0155/2674/d8a6d.png)
or![w^{2} -4w-96=0](/tpl/images/0155/2674/9ac4e.png)
=>![w^{2} -12w+8w-96=0](/tpl/images/0155/2674/1a1f5.png)
=>![w(w-12)+8(w-12)=0](/tpl/images/0155/2674/58638.png)
We get ,
; w = -8(neglect the negative value)
And length =
inches
Hence, dimensions are : L = 24 inches ; w = 12 inches and h = 4 inches
We can check by putting these values in equation :![256=(w+4)(w-8)(4)](/tpl/images/0155/2674/f90c4.png)
=>![256=(16)(4)(4)](/tpl/images/0155/2674/75c70.png)
=>![256=256](/tpl/images/0155/2674/8ce1c.png)
Ответ: