i have a piece of paper 22 in. long and 16 in. wide. i cut a 2 in. x 2 in. square from each corner. i then folds up the sides and forms a box with an open top. what is the volume of this box?
Since you cut a 2 in. x 2 in. square from each corner, you'll get a 2 in. height
The volume of the box will then be:
Vol = length x width x height
= 22 x 16 x 2
= 704 in^3
Note: the volume is the same for all cases, regardless of the condition of the lid (closed/open)
Since you cut a 2 in. x 2 in. square from each corner, you'll get a 2 in. height
Length now becomes = 22 - 4 = 18 in.
Width now becomes = 16 - 4 = 12 in.
The volume of the box will then be:
Vol = length x width x height
= 18 x 12 x 2
= 432 in^3
Note: the volume is the same for all cases, regardless of the condition of the lid (clos
ed/open)
To find the volume of the box, we first need to determine its dimensions after the corners are cut and the sides are folded.
Given:
Length of the paper = 22 inches
Width of the paper = 16 inches
Since we are cutting 2 inches from each corner, the dimensions of the base of the box (after folding) would be:
Length of base = Length of paper - 2*2 inches (two 2-inch corners are cut from both ends)
Width of base = Width of paper - 2*2 inches (two 2-inch corners are cut from both ends)
Length of base = 22 inches - 2*2 inches = 22 inches - 4 inches = 18 inches
Width of base = 16 inches - 2*2 inches = 16 inches - 4 inches = 12 inches
Now, the height of the box would be the length of the corner that was cut off, which is 2 inches.
Therefore, the volume of the box can be determined by multiplying the dimensions of the base and the height:
Volume = Length of base * Width of base * Height
Volume = 18 inches * 12 inches * 2 inches
Volume = 432 cubic inches
Hence, the volume of the box is 432 cubic inches.