Today, I am gonna describe the earth's rotational movement and its relation to a circle.

It takes the earth 24 hours to make a complete rotation. 24 hours is equals to 360 degrees in a circle. Now dividing the circle into 4 equal sectors each of 90 degrees, makes each sector equals to 6 hours, so it takes the earth 6 hours to rotate 90 degrees. Dividing each sector into 2 equal parts would give 3hrs and 45 degrees each. The polar radius of the earth is 6,357 km, so using area of a circle (note: I would be using # in place of pi):

#rr
# = 3.14
r = 6,357 km

3.14 * 6357 * 6357 = 126891949.9 cm2

The above result is the rotational area of the earth. The sectorial area reached by the earth during its rotation would be represented using area of a sector (I would be using @ in place of theta)

(@/360)#rr

Recall, a sector in this case is 90 degrees,

@ = 90 degrees

(90/360) * 3.14 * 6357 * 6357 = 31722987.47 cm2.

The above result is the sectorial area achieved by the earth's rotational movement within 6 hours and is 1/4 of the total area of its rotation.

In 3 hours the earth would have rotated an angle of 45 degrees and would have reached a sectorial area of 15861493.74 cm2 which is 1/2 of that reached by its rotation in 6 hours and 1/8 of its total rotational area.

Got questions about this? Bring them and I would gladly try to answer.

Since the rotational axis of the Earth is longitudinal, i.e, it rotates on it's polar axis, the relevant radius in your calculation should be the equatorial radius. This derives from the fact that distances and sectoral area measurements are done with reference to the equatorial and latitudinal circumferences.. ..... My take.

freeDR:
Since the rotational axis of the Earth is longitudinal, i.e, it rotates on it's polar axis, the relevant radius in your calculation should be the equatorial radius. This derives from the fact that distances and sectoral area measurements are done with reference to the equatorial and latitudinal circumferences.. ..... My take.

Thanks, I will work on that.