Packing Intuition Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy

A box is

30

cm long,

20

cm wide,

15

cm tall. How many

5\,\text{cm}

cubes can fit inside?

Solution

1
Step 1: Along length: $30/5 = 6$ . Along width: $20/5 = 4$ . Along height: $15/5 = 3$ .
2
Step 2: Total cubes $= 6 \times 4 \times 3 = 72$ .

Answer

72

cubes.

When packing identical cubes into a rectangular box, divide each box dimension by the cube side length to find how many fit in each direction, then multiply. This gives

100\%

packing efficiency since cubes tile perfectly.

About Packing Intuition

Arranging objects of given shapes to fit as many as possible into a bounded region without any overlapping.

Learn more about Packing Intuition →

More Packing Intuition Examples

Example 1 easy

Circular coins of radius [formula] cm are packed into a [formula] square tray in a square grid arran

Example 2 medium

Compare the packing efficiency of square packing ([formula]) vs hexagonal close packing ([formula])

Example 4 hard

Oranges of radius [formula] cm are packed in a square grid on a flat tray that is [formula]. A secon

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Area Volume Tessellation