Science Puzzle
How Many Earths Would Fit Inside the Sun?
The Sun is about 109 times wider than Earth: line up 109 Earths side by side and they'd just stretch across its face.
If the Sun were a hollow ball, roughly how many Earths could you fit inside it?
The Answer
About 1.3 million. Make something 109 times wider in every direction and its volume grows by 109 × 109 × 109.
109 Earths fit across the Sun in a line. To cover the flat face of the Sun, you'd need about 109 rows of 109, around 12,000 Earths. But the Sun is a ball, not a disc, so you also need about 109 layers of those. That's 109 × 109 × 109, about 1.3 million. (Solid balls leave gaps when you pack them, so if the Earths had to stay round, a little under a million would actually fit. Melt them down and pour them in, and it's 1.3 million.)
The same rule works for anything. Double the width of a cube and it holds eight times as much; a pizza twice as wide has four times as much pizza. This is why volume grows so fast as things get bigger.
The Sun isn't as heavy as its size might suggest, though. It's made mostly of hydrogen and helium, so on average it's much less dense than Earth. It's about 333,000 times as massive as Earth: still enough to make up about 99.8% of the mass of the whole Solar System.
The principle: Scaling. When an object is scaled up, its area grows with the square of its width and its volume with the cube, so volume increases far faster than width.