We have a section of the sphere with height h. If we slice it into n slices, each with height h/n, then the surface area of each one will be about 2πrh/n, so in total, the area will be about n×2πrh/n=2πrh.

The total area of segment of a sphere is equal to area of the zone plus the sum of the areas of the bases. V=13πh2(3R−h) (okay!)

NO! There are no parallel lines in spherical geometry.

Parallel lines are lines in a plane that are always the same distance apart. Perpendicular lines are lines that intersect at a right (90 degrees) angle. Created by Sal Khan and Monterey Institute for Technology and Education.

Because of the fact that the sum of the three interior angles of a triangle must be 180 degrees, a triangle could not have two right angles.

Any two great circles intersect in two opposite points. So there are no parallel “lines” (great circles) on a sphere. On the beach ball example, we saw great circles that look like longitude circles through the north and south poles on a globe.

A great circle has the same circumference, or outer boundary, and the same center point as its sphere. The geometry of spheres is useful for mapping the Earth and other planets. The Earth is not a perfect sphere, but it maintains the general shape. All the meridians on Earth are great circles.

a circle on the surface of a sphere which lies in a plane passing through the sphere’s centre. As it represents the shortest distance between any two points on a sphere, a great circle of the earth is the preferred route taken by a ship or aircraft.

Latitude varies from 0 degrees (equator) to 90 degrees north and south (the poles). A line connecting all points of the same latitude is called a parallel, because the lines run parallel to each other. The only parallel that is also a great circle is the equator. Tropic of Cancer, 23.5 degrees N.

What are the three heat zones of the Earth? |NCERT Geography class 6

• Torrid Zone.
• Temperate Zone.
• Frigid Zone.

The oblate spheroid, or oblate ellipsoid, is an ellipsoid of revolution obtained by rotating an ellipse about its shorter axis. It is the regular geometric shape that most nearly approximates the shape of the Earth. A spheroid describing the figure of the Earth or other celestial body is called a reference ellipsoid.

geoid

identifying the main components of the earth system: the geosphere, atmosphere, hydrosphere and biosphere.

oblate spheroid

There are many reasons why the geoid isn’t a sphere. First and foremost, the Earth itself isn’t a sphere. It is closer to an ellipsoid, being flattened at the poles by the centrifugal force of its own rotation. That mass distribution affects the gravitational field and makes the geoid asymmetrical too.

Earth is a sphere or, more correctly, an oblate spheroid, which is a sphere that is a bit squished down at the poles and bulges a bit at the Equator.