Inside the hive

Inside a hive, honey is stored in wax cells, and every cell is a hexagon, a shape with six equal sides. Hexagons fit together with no gaps, so no wax is wasted.

Honey is stored in wax cells, and each cell is a hexagon: $6$ equal sides. Hexagons fit together with no gaps, so no wax is wasted.

cell: hexagon $H$, $6$ sides.

Why no gaps? Each corner of a hexagon is one hundred and twenty degrees. Three corners meet at every point, and three times one hundred and twenty is three hundred and sixty, a full turn.

Each corner is $120^{\circ }$. Three meet at a point: $3\times 120^{\circ }=360^{\circ }$, a full turn, so there is no gap.

gap $g$: $3\times 120^{\circ }=360^{\circ }\Rightarrow g=0$.

A worker bee visits about one hundred flowers on every trip, and she makes about ten trips a day. That is a thousand flowers a day for one small bee.

A worker visits about $100$ flowers per trip and makes about $10$ trips a day: $100\times 10=1000$ flowers a day.

one bee, one day: $100\times 10=1000$.

A busy hive sends out twenty thousand foragers. Twenty thousand times a thousand is twenty million flowers in a single day.

A busy hive sends out $20000$ foragers: $20000\times 1000=20000000=2\times 10^7$ flowers a day.

$20000\times 1000=2\times 10^7$.