Question

Find the altitude of a zone whose area is 240pi sq. u. if the circumference of a great circle is 24pi units.

Answer 1

I think you mean "latitude" instead of "altitude." I think you are asking about the area of a region bounded by two lines of latitude.

This appears to be a mathematics question.

If the circumference of a great circle is 2πR = 24π units then the radius of the circle is R = 12 units. The surface area of the sphere is 4πR^2 = 4*π*12^2 = 576π sq. units.

At a latitude λ the circumference of a line of latitude is Ccosλ where C = 24π is the circumference of a great circle. The area of a narrow strip of width dS at latitude λ is dA = CcosλdS. But dS = Rdλ, so
dA = Ccosλ.Rdλ
= 24π.12.cosλdλ
= 288π cosλdλ.
The area between lines of latitude λ1 and λ2 is the integral of this expression, viz.
A = 288π(sinλ2-sinλ1).
This area must equal 240π, so
sinλ2-sinλ1 = 240/288 = 5/6.
To solve the problem we need to one one of the two boundary lines of latitude. Possibly you are assuming that they are symmetrical about the equator, ie λ1 = -λ2. If so then
2sinλ2 = 5/6
sinλ2 = 5/12 = 0.416667
sinλ2 = 0.429775 radians = 24.6°.
ie the area between latitude lines -24.6° and +24.6° is 240π sq. units.

Answer 2

Don't ask me what those boxes are all about?!

Answer 3

Its alitude , i need to find the height