MATH Q: Find the size of the original square if the resulting tray has a volume of 128 cu in.?

Question

A square piece of cardboard was used to construct a tray by cutting 2-inch squares out of each corner and turning up the flaps. Find the size of the original square if the resulting tray has a volume of 128 cu in.

Answer 1

this belongs in homework help

Answer 2

The tray is a rectangular prism. The formula for the volume of a triangular prism is: length times width times height, or in symbolic terms:
L x W x H = V

you know your height is 2 inches. (this is the width of the flaps). Also, because your original piece of cardboard is a square, and you cut a two inch square out of all four corners, the length = width. so the tray has 4 sides of equal length. Your equation is

128 = 2 x s^2 (where s = side of the tray)

solving this equation:
128/2 = (2 x s^2)/2
64 = s^2
s = 8

So each side of the tray is 8 inches. To find the length of the side of the original square, you have to add 4 inches (because that's the amount of length you cut off each side when you cut those four 2-inch squares out of the corners of the cardboard.)

So your original piece of card board is a square with each side having a length of 12 inches.

Answer 3

volume of a prism is given by length x width x height
since the resulting tray has a square base, the width and length of the prism is equal to each other. (width = length). the height is also given: 2 inches. then, the volume would be like this:
*let x be width or length*
(x^2)(2) = 128
x^2 = 64
x = 8
since 8 inches was the dimension of the width and length of the tray, we just add four inches to get the original size of the square.
width, length of square = 12 inches,
which gives an are = 144 square inches.

Answer 4

Draw a figure and label its dimensions. (x-4)(x-4)2 = 128

(x-4)(x-4)=64

x-4 = 8
x = 12

Answer 5

r u cheating on homework dude?

Answer 6

dunno . . . do ur own homework . . .