Practice Packing Intuition in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Arranging objects of given shapes to fit as many as possible into a bounded region without any overlapping.
How many oranges can you stack in a box? How to arrange them?
Example 1
easyCircular coins of radius 1 cm are packed into a 10\,\text{cm}\times 10\,\text{cm} square tray in a square grid arrangement. How many coins fit and what is the packing efficiency?
Example 2
mediumCompare the packing efficiency of square packing (\pi/4) vs hexagonal close packing (\pi/(2\sqrt{3})) of unit circles. Which is more efficient and by how much?
Example 3
easyA box is 30 cm long, 20 cm wide, 15 cm tall. How many 5\,\text{cm} cubes can fit inside?
Example 4
hardOranges of radius 4 cm are packed in a square grid on a flat tray that is 40\,\text{cm}\times 40\,\text{cm}. A second layer is placed on top in hexagonal arrangement offset by 4 cm in each direction. How many oranges are in the first layer? How many extra fit in the second layer?