Hemisphere

A hemisphere is a 3D geometric figure that is half of a sphere (hemi- means half).

Earth can be divided into the Northern Hemisphere and the Southern Hemisphere. It can also be divided into the Eastern Hemisphere and the Western Hemisphere.

Properties of a hemisphere

In Geometry, a hemisphere is created by a plane intersecting a sphere through the sphere's center.

In the figure above, plane P intersects sphere O through its center, creating two hemispheres of equal size. Since a hemisphere is half of a sphere, they share many of the same properties.

Radius

A radius, r, of a hemisphere is a line segment from the center of the hemisphere to a point on the hemisphere's surface. A few radii (plural for radius) are graphed for the hemispheres with center at point O below.

Diameter

Like a sphere, a diameter of a hemisphere is any chord that passes through its center, as shown below.

Great circle

A great circle is a circle formed when a plane intersects a sphere through its center. It divides a sphere into two equal halves, known as hemispheres.

One of the hemispheres for a sphere is shown above. The great circle of the sphere is the base of the hemisphere.

Surface area of a hemisphere

The total surface area of a hemisphere is the sum of the areas of its circular base and its curved surface.

S = 3πr²

where r is the radius of the hemisphere.

The area of the circular base of a hemisphere with radius r is πr². The area of the curved surface of the hemisphere is one-half the surface area of a sphere. The surface area of a sphere is 4πr², so the area of the curved surface of the hemisphere is 2πr².

The total surface area, S, of the hemisphere is S = πr² + 2πr² = 3πr².

Volume of a hemisphere

The volume of a sphere is . Since a hemisphere is half of a sphere, its volume, V, is half the volume of a sphere, so

where r is the radius of the hemisphere.