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Earth and Space · Chapter 2: Structure of the Earth

Shape and Size of the Earth

The Earth is an oblate spheroid with an average radius of 6,371 km. Evidence that the Earth is round, and Al-Biruni's method of measuring its radius, with a virtual lab.

Taught in Class 9Class 10O Level

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01Concept

The Earth is almost a sphere, but not quite. Because it spins, it bulges slightly at the equator and is a little flattened at the poles. This shape is called an oblate spheroid.

The Earth is slightly wider at the equator than from pole to pole (exaggerated here).
MeasurementValue (rounded)
Equatorial radius6,378 km
Polar radius6,357 km
Average radius6,371 km
Circumference at the equatorabout 40,075 km
Surface areaabout 510 million km²

Evidence that the Earth is round

  1. Ships at sea: as a ship sails away from Karachi port, its hull disappears first and the top of its mast last, as it goes over the curve.
  2. Lunar eclipse: the Earth's shadow on the Moon is always curved. Only a sphere always casts a round shadow.
  3. Photos from space: satellites and astronauts see a round Earth.
  4. Different stars: travelling north or south, the Pole Star rises higher in the sky in Gilgit than in Karachi.
  5. Time zones: the Sun rises at different times in different places because the Earth is a turning ball.

How the size of the Earth was measured

Eratosthenes (Greece, about 240 BCE) compared the length of shadows in two Egyptian cities to estimate the Earth's circumference. About 1,250 years later, Al-Biruni found a cleverer way that needed only one place: a hill near the sea or a flat plain.

  1. He measured the height of a hill near Nandana Fort in today's Jhelum district, using trigonometry.
  2. From the top, he measured how far the horizon looked below the level line. This small angle is the dip angle (θ).
  3. (O Level) Because the line of sight touches the Earth at the horizon, it makes a right angle with the radius. So cos θ = R ÷ (R + h), which rearranges to R = h cos θ ÷ (1 − cos θ).
  4. His result, about 6,340 km, is within about 0.5% of the modern value.

02Virtual Lab

Try this topic for yourself in the virtual lab. It opens on its own page with steps, tasks and questions.

ExperimentMeasure the Earth like Al-BiruniUse Al-Biruni's own measurements from a hill near Nandana Fort and work out the radius of the Earth.Extension: Class 10 / O LevelOpen the lab →

03Key Formulas

Al-Biruni's method (O Level extension)

R=hcos⁡θ1−cos⁡θR = \frac{h\cos\theta}{1-\cos\theta}
  • RR = radius of the Earth (same unit as h)
  • hh = height of the hill (m or km)
  • θ\theta = dip angle of the horizon

From cos θ = R ÷ (R + h), because the line of sight to the horizon is a tangent.

Circumference of the Earth

C=2πRC = 2\pi R

With R = 6,371 km, C ≈ 40,030 km (the equator is a little longer, 40,075 km).

04Real World Examples

Ships disappearing

Watch a ship leave Karachi or Gwadar port: the bottom disappears first, a simple everyday proof that the Earth is curved.

GPS needs the true shape

Navigation systems use the Earth's exact oblate shape. Treating it as a perfect sphere would put you hundreds of metres off.

Flight routes

Planes from Karachi to North America fly over the far north because, on a round Earth, that is the shortest path.

Seeing farther from high places

From the top of a tall building or a hill you can see much farther before the curve hides the ground: the idea behind Al-Biruni's method.

05Practice Questions

Try to answer in your own words first, then open the model answer.

Short questions

Q1.What is the shape of the Earth called? Why is it not a perfect sphere?Show answer

Answer

The Earth is an oblate spheroid. Because it spins on its axis, it bulges slightly at the equator and is flattened at the poles.

Q2.Give three pieces of evidence that the Earth is round.Show answer

Answer

  • A ship sailing away disappears hull first.
  • The Earth's shadow on the Moon during a lunar eclipse is always curved.
  • Photos from space show a round Earth.
Q3.What is the dip angle?Show answer

Answer

The dip angle is the small angle between the level (horizontal) line and the line of sight to the horizon, measured from a high point such as a hilltop.

Q4.(O Level) From a hill 500 m high, the dip angle is 0.7177°. Find the radius of the Earth. (cos 0.7177° = 0.999921547)Show answer

Answer

  • R = h cos θ ÷ (1 − cos θ)
  • R = 0.5 km × 0.999921547 ÷ (1 − 0.999921547)
  • R = 0.49996 ÷ 0.000078453 ≈ 6,373 km

Long questions

Q5.Explain how Al-Biruni measured the radius of the Earth. Draw a labelled diagram.Show answer

Answer

  1. He found the height (h) of a hill near Nandana Fort using trigonometry.
  2. From the top, he measured the dip angle (θ) between the level line and the horizon.
  3. The line of sight to the horizon touches the Earth, so it is at 90° to the radius. In the right-angled triangle formed by the centre, the horizon point and the hilltop: cos θ = R ÷ (R + h).
  4. Rearranging: R = h cos θ ÷ (1 − cos θ).
  5. He got R ≈ 6,340 km, very close to the modern 6,371 km.

Diagram: draw a circle (Earth) with centre O, a hill of height h on top, a line from the hilltop touching the circle (the horizon), the level line from the hilltop, the angle θ between them, and the two radii R.

06Quiz

Question 1 of 8
The shape of the Earth is best described as:

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