Describe the measurement of Earth's shadow (umbra) radius during total lunar eclipse.

Explanation

It is possible to measure the radius of shadow of the Earth at the point where the Moon crosses. When the Moon exits from the umbra shadow, it appears red in color. As soon as the Moon exits from the umbra shadow, it appears in crescent shape.
By knowing the apparent radii of the Earth's umbra shadow and the Moon, the ratio of the these radii can be calculated.
The apparent radius of Earth's umbra shadow `=R_(s)=13.2cm`.
The apparent radius of the Moon `=R_(m)=5.15cm`.
The ratio `(R_1)/(R_m)~~2.56`
The radius of the Earth's umbra shadow is,
`R_(s)=2.56xxR_(m)`
The radius of Moon `R_(m)=1737km`
The radius of the Earth's umbra shadow is,
`R_(s)=2.56xx1737km~=4446km`
The correct radius is 4610 km.