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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Ball Packing

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### Three Balls

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### Mouhefanggai

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Age 14 to 16

Challenge Level

- Problem
- Student Solutions

If a ball is rolled into the corner of a room how far is its
centre from the corner?
A sphere of diameter $10$cm is packed into a cubic box whose internal side lengths are $12$cm. To prevent the sphere from rolling around 8 identical smaller spheres are placed in the corners of the box. What is the radius of one of the smaller spheres? |

A circle has centre O and angle POR = angle QOR. Construct tangents at P and Q meeting at T. Draw a circle with diameter OT. Do P and Q lie inside, or on, or outside this circle?

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.