A manufacturer sells widgets, each of which is packaged in a box whose dimensions are 8 centimeters by 8 centimeters by 8 centimeters. Design the dimensions of a box to ship widgets. Your box must hold at least 1000 widgets. (Enter your answer in the form length, width, height. Give all dimensions in centimeters.)

Well, if we assume that the widgets are obedient and don't mind being stuffed together like sardines, let's get creative with our box design!

To hold at least 1000 widgets, we could try a box with dimensions 80 centimeters by 80 centimeters by 10 centimeters! This way, we have enough space for the widgets without them feeling too cramped.

Of course, now the box might need a personality adjustment, as it might feel a tad too long and flat. But hey, it's all about accommodating those widgets, right?

To design a box that can hold at least 1000 widgets, you'll need to calculate the volume of one widget box and use that to determine the dimensions of the shipping box.

Step 1: Calculate Volume of One Widget Box
Since the dimensions of one widget box are 8 cm by 8 cm by 8 cm, the volume can be calculated as:
Volume = Length x Width x Height
Volume = 8 cm x 8 cm x 8 cm
Volume = 512 cm³

Step 2: Determine Dimensions of Shipping Box
To hold at least 1000 widget boxes, we need a shipping box with a volume of at least 1000 times the volume of one widget box.
Shipping Box Volume = 1000 x Widget Box Volume
Shipping Box Volume = 1000 x 512 cm³
Shipping Box Volume = 512,000 cm³

Step 3: Calculate Dimensions of Shipping Box
Now, we need to find the dimensions of the shipping box that has a volume of 512,000 cm³.
Assuming the dimensions of the shipping box can be different, let's assign the dimensions as:
Length = L cm
Width = W cm
Height = H cm

From the volume formula, we can set up the equation:
Shipping Box Volume = L x W x H
512,000 cm³ = L cm x W cm x H cm

Since we don't have any other constraints, there are multiple solutions for the dimensions. However, some possible dimensions that satisfy the requirement are:
Length = 80 cm, Width = 64 cm, Height = 10 cm
Length = 160 cm, Width = 32 cm, Height = 10 cm
Length = 400 cm, Width = 16 cm, Height = 10 cm
...and so on.

Please note that these are just a few examples, and you can vary the dimensions as long as the volume of the shipping box is at least 512,000 cm³.

To design the dimensions of a box that can hold at least 1000 widgets, we need to calculate the volume of one widget and then determine the volume capacity of the box considering the number of widgets.

The volume of one widget can be calculated by multiplying its dimensions: 8 cm x 8 cm x 8 cm = 512 cm³.

To find the volume capacity required for 1000 widgets, we multiply the volume of one widget by the number of widgets: 512 cm³/widget x 1000 widgets = 512,000 cm³.

Since the box needs to hold at least this amount of volume, we can consider the box dimensions in a way that they meet or exceed the required capacity. Here is one possible box dimension solution:

Length: 80 centimeters
Width: 40 centimeters
Height: 32 centimeters

To calculate the volume of this box, we multiply its dimensions: 80 cm x 40 cm x 32 cm = 102,400 cm³.

Therefore, this box with dimensions 80 cm x 40 cm x 32 cm (length, width, height) can hold at least 1000 widgets, as its volume capacity is 102,400 cm³, which exceeds the required 512,000 cm³.

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