An open box is to be constructed from a rectangular sheet of tin 3 meters wide by cutting out a 1-meter square from each corner and folding up the sides. The volume of the box is to be 2 cubic meters. What is the length of the tin rectangle?
V = area of base * height
Since 1m was cut from each corner, the base is just 1m wide now. Likewise, since the cut was 1m deep, the height is now 1m.
So, the volume = width * height * length
2 = 1 * 1 * length
what, oh, what could be the length?
2? NO! That's the length of the box. The tin sheet has to be 4m long, so the 1m corners can be cut out.
Algebra - tchrwill, Tuesday, October 4, 2011 at 10:40am
Draw a picture showing width = 3 and
Draw the corner cutouts.
Label the length of each edge
If the total length of the sheet is X,
Then, (X - 2)(1)(1) = 2 making X = 4 meters.
V = area of base * height
Since 1m was cut from each corner, the base is just 1m wide now. Likewise, since the cut was 1m deep, the height is now 1m.
So, the volume = width * height * length
2 = 1 * 1 * length
what, oh, what could be the length?
2? NO! That's the length of the box. The tin sheet has to be 4m long, so the 1m corners can be cut out.
Draw a picture showing width = 3 and
Draw the corner cutouts.
Label the length of each edge
If the total length of the sheet is X,
Then, (X - 2)(1)(1) = 2 making X = 4 meters.
To find the length of the tin rectangle, we need to set up and solve an equation based on the given information.
Let's start by visualizing the rectangular sheet of tin before any cuts are made:
```
__________________
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| |
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|________________|
```
The width of the tin rectangle is given as 3 meters (since it is 3 meters wide).
Now, we are instructed to cut out a 1-meter square from each corner:
```
____1____ ____1____
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| | |
| | |
|________|________|
```
After making these cuts, we can fold up the sides to form an open box:
```
____1____ ____1____
| | |
| | |
| | |
| | |
|________|________|
```
Now, we are told that the volume of the box should be 2 cubic meters. The volume of a rectangular box is given by the formula length × width × height.
In this case, since the box is open at the top, the height is the same as the length of the cut-out squares. Hence, the height of the box is 1 meter.
Let's denote the length of the tin rectangle as L. After folding up the sides, the resulting length of the box will be L - 2 (since we removed two 1-meter squares).
Therefore, the volume of the box is (L - 2) × 3 × 1 = 2.
Now, we can set up and solve the equation:
(L - 2) × 3 = 2
First, let's distribute the 3:
3L - 6 = 2
Next, let's isolate L:
3L = 2 + 6
3L = 8
Dividing both sides by 3:
L = 8/3
So, the length of the tin rectangle is 8/3 meters, or approximately 2.67 meters.