SOLUTION: A manufacturer of globes that are approximately 1 m in diameter packs the globes in 1-cubic- meter boxes for shipping. How much packing material (foam peanuts) is needed for a ship

Question 1068253: A manufacturer of globes that are approximately 1 m in diameter packs the globes in 1-cubic- meter boxes for shipping. How much packing material (foam peanuts) is needed for a shipment of 100 globes?
Answer by Lightning_Fast(78) (Show Source): You can put this solution on YOUR website!
Let's start off with what we are given:
- Globes are 1 meter in diameter
- Globes are packed in 1 meter cubed boxes. 1 meter cubed boxes can also be written as:
What we need to find:
- The amount of packing material for 100 globes.
To start this problem, we will figure out the packing material for one globe, them multiply it by 100.

.
Above is a diagram that represents the situation. The blue is the globe. The box around the globe represents the shipping boxes. The space in between the globe and the shipping box is red, or where the packing materials, or the foam peanuts fit.
NOTE: This diagram is a 2D representation of this 3D problem.
To find this area, we need to subtract the volume of the circle FROM the volume of the box.
In other words, volume of the box - volume of the circle = volume of packing material
Note: For this material, we must assume the packing material is distributed at the same density throughout the box.
Volume of the box: 1meters
Volume of circle:
Since radius is half the diameter, the radius of the sphere, or globe is 1/2 meters. Therefore, we plug in the radius to get the area of the circle.
Volume of the circle:
Volume of the circle: (remember, this is volume, so the units are meters cubed, or
Before, we know the solution was:
volume of the box - volume of the circle = volume of packing material
Let plug in the known values now!
= volume of the packing material
= volume of the packing material
= volume of the packing material
Don't forget we have 100 of these globes, so

Thus, you would write: The volume of the packing material for 100 1-meter-diameter globes is about 47.64 meters cubed.
You can also write it like this:

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