An open box is to be constructed from a rectangular sheet of tin 5 meters wide by cutting 1 square
meter from each corner and folding up the sides. The volume of the box is to be 18 cubic meters.
What is the length of the tin rectangle?
Volume = w * h * L
18 = (5-2) * 1 * L
Solve for L.
To find the length of the tin rectangle, we can use the formula for the volume of a rectangular box:
Volume = Length × Width × Height
Given that the volume of the box is 18 cubic meters, we need to find the length of the tin rectangle.
Let's assume that the length of the tin rectangle is x meters.
When we cut a 1 square meter from each corner, the resulting box will have a width of (5 - 1 - 1) = 3 meters and a length of (x - 1 - 1) = (x - 2) meters.
Folding up the sides will create a height of 1 meter.
So, we can write the equation as:
18 = (x - 2) × 3 × 1
To solve for x, we divide both sides by 3:
18 ÷ 3 = (x - 2) × 1
6 = x - 2
Now, we can solve for x by adding 2 to both sides:
6 + 2 = x
x = 8
Therefore, the length of the tin rectangle is 8 meters.