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An introduction to exoplanets
An introduction to exoplanets

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The equation for the area of a circle

The area of a circle is related to the radius of the circle, just as the volume of a sphere is related to the radius of the sphere as you saw in Week 2. Remember that the radius of the two-dimensional circle we see as a star is actually the same as the radius of the three-dimensional, spherical star itself.

It has been known since at least the time of the ancient Babylonians that the area of a circle is a little more than three times its radius squared. To find the exact area of a circle the radius squared is multiplied by a numerical constant called ‘pi’, which has the symbol π and is pronounced ‘pie’. Pi is close to the value 3.14, but if you have a calculator with a ‘π’ button it’s best to use that when working out areas and volumes.

So, the area of a circle is given by:

area equation left hand side equals right hand side pi postfix multiplication radius multiplication radius
Equation label: (Equation 1)

which can also be written as:

cap a equals pi times r squared
Equation label: (Equation 2)

This is shown in Figure 13.

Figure 13  Area of a circle with radius r

For example, the area of a circle with a radius of 10 m would be

equation sequence pi multiplication 10 squared equals pi multiplication 10 multiplication 10 equals 314 normal m squared

Generally, you measure area in m2 or cm2.

The cross-sectional area of a sphere with radius 10 m would also be 314 m2.