Question About Circles

[maxinewolph]

Im terrible at math and Im working on creating a building model for a sustainable living project.

so my question for the math peoples out there is,

If I have a Sphere, cut directly in Half (the building would be a dome structure)

If the very base of the dome structure is 70ft, I looked it up online and it said total height would be something like 34ft.

But If I put a floor 10ft above base level, and another floor 10ft above that one (so a basement,main floor, and Second floor)

If the Base Floor is 70ft across, what would the next two floors be across???

siply have no idea how to do this type of math, and would greatly appreciate any help : )

Sincerly, Maxine Wolph

 

[DrPhil]

Im terrible at math and Im working on creating a building model for a sustainable living project.

so my question for the math peoples out there is,

If I have a Sphere, cut directly in Half (the building would be a dome structure)

If the very base of the dome structure is 70ft, I looked it up online and it said total height would be something like 34ft.

But If I put a floor 10ft above base level, and another floor 10ft above that one (so a basement,main floor, and Second floor)

If the Base Floor is 70ft across, what would the next two floors be across???

siply have no idea how to do this type of math, and would greatly appreciate any help : )

Sincerly, Maxine Wolph

Picture a globe that you have cut in half at the equator. If the diameter of the base is 70 feet, then the height is a radius, exactly half of the diameter, or 35 feet.

If you put a floor at 10 feet, you can use the "good old" Pythagorean theorem to find the radius at that latitude. Do you remember c^2=a^2+b^2 for a right triangle? in this case "c" is the radius of the sphere, or c=35', a is the elevation, a=10', and b is the unknown radius of the floor at elevation a. [BTW, ^2 means squared.]
b^2 = c^2 - a^2 = 1125 ft^2
and the area of that floor is the area of a circle:
A @ 10' = pi b^2 = 3534 sq.ft.
diameter @ 10' = 2b = 67'

Likewise if a = 20', then
b^2 = (35')^2 - (20')^2 = 825 ft^2
A @ 20' = 2592 sq.ft.
diameter @ 20' = 2b = 57'

Again looking at the globe, I will tell you that 10' elevation corresponds to a latitude circle at 16.6°,
and the elevation 20' is latitude 53.1°.

 

[maxinewolph]

thank you

I see I was thinking very 2D for getting the height of my half circle

I appreciate the help very much : )

Sincerely, Maxine Wolph