SOLUTION: An open box is to be made from a rectangular piece of tin by cutting two inch squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. F
Algebra.Com
Question 115523: An open box is to be made from a rectangular piece of tin by cutting two inch squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular piece of tin.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
An open box is to be made from a rectangular piece of tin by cutting two inch squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular piece of tin.
:
There are many dimensions that will satisfy this requirement.
:
Let x = width; y = length of the rectangular piece tin
:
We know the height will be 2inches, then the base will = 100/2 = 50 sq/in
:
The base dimension will be (x-4) by (y-4)
:
write an equation where y is the length and x = width
:
(x-4)(y-4) = 50
FOIL
xy - 4y - 4x + 16 = 50
:
xy - 4y = 50 + 4x - 16
:
y(x-4) = 4x + 34
:
y =
:
With this equation you can substitute any value greater than 4 for x (width)
y = length for that width which will give you 100 cu inches
:
Sticking to integers: let x = 9"
:
y =
y =
y = 14"
;
Check the box dimensions: (14-4)*(9-4)*2 = 100 cu in
:
Let x = 29"
y =
y =
y = 6"
:
Check box dimensions: (29-4)*(6-4)*2 = 100 cu in
RELATED QUESTIONS
An open box is to be made from a rectangular piece of tin by cutting two inch squares out (answered by 303795)
An open box is to be made from a rectangular piece of tin by cutting two inch squares out (answered by checkley77)
An open box is to be made from a rectangular piece of tin by cutting 2-inch squares out... (answered by josgarithmetic)
An open-top box will be made from a square piece of cardboard of length 26-inch by... (answered by ankor@dixie-net.com)
A rectangular piece of tin 40cm by 30cm is to be made into an open box with a base of... (answered by josgarithmetic)
Here is the question I have:
An open-top box will be made from a square piece of... (answered by Earlsdon)
An open box is to be constructed from a 12 x 12 inch piece of board by cutting away... (answered by Fombitz,ikleyn)
n open box will be made out of a piece of metal that is 24 inches by 30 inches by cutting (answered by Earlsdon)
An open top box is to be constructed out of a 85 inch by 120 inch piece of cardboard by... (answered by greenestamps)