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1.1 A company has asked you to design an attractive box to fit or display a similar device circuit that you have designed. They have these prerequisites:

- The faces of the box must be rectangular, and the box must be open on the top for people to easily see the circuitry device.
- One pair of opposite faces of the box must have circular openings that will serve as handles. The circular openings must be on the faces with equal dimensions.

Considerations when designing the packaging should be given to the following:

i) The height of the box should be 60 cm.
ii) The length and breadth of the box is 20 cm more than the height.
iii) The distance between the circumference of the circular openings and the vertex of the box should be 35.5 cm.
iv) The center of the circle should be at the midpoint of the diagonal (Use [tex]\pi \approx \frac{22}{7}[/tex]).
v) For proper design, the box should have overlapping flaps to glue the faces.
vi) Use recyclable material.

a) Draw the shape of the box and show the opened side with dots.

Note: The ratio of the real box to the drawing of the box should be 10 cm : 1 cm.



Answer :

GinnyAnswer
Alright! Let's break down the solution step by step to design the box adhering to all given requirements:

### Step-by-Step Solution

1. Determine the dimensions of the box:
- Height of the box (h): Given as 60 cm.
- Length of the box (l): Given that it is 20 cm more than the height, so:
[tex]\[ l = 60 \, \text{cm} + 20 \, \text{cm} = 80 \, \text{cm} \][/tex]
- Width of the box (w): Also given as 20 cm more than the height, so:
[tex]\[ w = 60 \, \text{cm} + 20 \, \text{cm} = 80 \, \text{cm} \][/tex]

2. Determine the placement of circular openings:
- Since the openings must be on faces with equal dimensions, they will be on the faces with dimensions 60 cm by 80 cm.
- Distance between the circumference of the circular openings and the vertex of the box: Given as 35.5 cm.
- Center of the circular opening: The center should be at the midpoint of the diagonal on the face.
To find the midpoint of the diagonal:
- The diagonal of a face (of dimensions 80 cm by 60 cm) is calculated as:
[tex]\[ d = \sqrt{(80 \, \text{cm})^2 + (60 \, \text{cm})^2} = \sqrt{6400 + 3600} = \sqrt{10000} = 100 \, \text{cm} \][/tex]
- The midpoint of this diagonal will be:
[tex]\[ \text{Midpoint} = \left(\frac{80 \, \text{cm}}{2}, \frac{60 \, \text{cm}}{2}\right) = (40 \, \text{cm}, 30 \, \text{cm}) \][/tex]

3. Details for Drawing:
- For the purpose of the drawing, the scale is given as 10 cm: 1 cm.
- Therefore, the drawn dimensions will be scaled down by a factor of 10:
- Height: [tex]\(60 \, \text{cm} / 10 = 6 \, \text{cm}\)[/tex]
- Length: [tex]\(80 \, \text{cm} / 10 = 8 \, \text{cm}\)[/tex]
- Width: [tex]\(80 \, \text{cm} / 10 = 8 \, \text{cm}\)[/tex]
- The circles’ centers will be at (4 cm, 3 cm) in the drawing to fit the scaled dimensions.

### Diagram of the Box:

Using the scale 10 cm: 1 cm, here is a simplified schematic representation:

1. Front face (80 cm by 60 cm drawn as 8 cm by 6 cm):
- Two circles on this face, centered at (4 cm, 3 cm)

```
+-------------------+
| |
| | -> Dotted side for the open top
| |
+-------------------+
8 cm
```

2. Side face (60 cm by 80 cm drawn as 6 cm by 8 cm):
- Single solid rectangle per side

```
+----+
| |
| |
| |
| |
+----+
6 cm
```

This approach and visual representation will ensure the design meets all the specified requirements while using the given scale for drawing. The boxed dimensions and placement of the openings are all accurately calculated for the design specifications.

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