Question

Answer? ................,,,,,,

Answer 1

Explanation:

what is the formula for the whole surface area of a sphere ?

`a = 4 * \pi * {r}^(2)`

that would give us the whole surface area all 360 degrees or 2×pi arc length all around the sphere.

but we don't need all 360 degrees. we only need the Theta'th (that is the specified angle) part.

in radians the arc length of that angle segment on the "equator" of the sphere

s = r×Theta

and the whole equator circumference is

c = 2×pi×r

so, the Theta'th part is then

r×Theta / 2×pi×r = Theta / 2×pi

we only need that part of the whole sphere surface area, so the formula would look like

`lune = theta * 4 * \pi * {r}^(2) / (2 * \pi)`

=>

`lune = theta * 2 * {r}^(2)`