Question

• Take an orange and peel off its skin. You will see the segments inside and thin vertical lines on them.
• Carefully take out one segment. Observe the segment and the gap it has left in the orange. See figure.
• See if the shape of the central and terminal portions of the segment is the same or different.
• See if the angle of the gap is the same at all points.
• Find how many segments are there in an orange.

Answer 1

• After peeling off the skin, the orange is seen to be made up of many wedge-shaped segments. The thin vertical lines separating the segments look like the meridians of longitude drawn on a globe. Just as meridians divide the earth into sections, these lines divide the orange into segments.
• Each segment is flat on the inner side, curved on the outer side and tapers towards both ends. The gap left behind has exactly the same shape as the segment that was taken out. This gap looks like the space between two adjacent meridians on a globe.
• The shape of the central and terminal portions is different. The central (middle) portion of the segment is broad and wide, while the terminal (end) portions are narrow and pointed. This shows that the gap between two meridians is the widest in the middle (at the equator) and goes on decreasing towards the two ends (the poles), where it becomes zero.
• Yes, the angle of the gap is the same at all points. The walls of the segments meet at the centre of the orange at the same angle. In the same way, the angular distance between two meridians measured at the centre of the earth remains the same, even though the actual distance between them goes on decreasing towards the poles.
• An orange generally has 10 segments (the number may vary slightly from orange to orange). The cross section of an orange is a circle, and there are $$360^{\circ}$$ in a circle. So each segment covers $$\frac{360^{\circ}}{10} = 36^{\circ}$$ at the centre. This is similar to the way the $$360^{\circ}$$ of the spherical earth are divided into meridians of longitude.