Hemisphere

A hemisphere is each of the parts obtained by cutting a sphere by a plane through its center.

Hemisphere

Surface Area of a Hemisphere

Area of a Hemisphere Formula

Volume of a Hemisphere

Volume of a Hemisphere Formula

Examples

The dome of a cathedral has a hemispherical form with a diameter of 50 m. If the restoration costs $300 per m2, what is the total cost of the restoration?

Hemisphere Exercise

15,707.96 · 300 = $4,712,388.98

Calculate the volume of a hemisphere with a radius 10 cm.

Hemisphere Exercise


Spherical Wedge

Spherical Wedge


The spherical wedge is the part of a sphere between two planes which intersect at the diameter.

Volume of a Spherical Wedge

Volume of a Spherical Wedge

Volume of a Spherical Wedge Formula

Spherical Lune


The spherical lune is the surface area of a sphere between two planes which intersect at the diameter.

Area of a Spherical Lune

Area of a Spherical Lune Formula


Spherical Cap

Spherical Cap

A spherical cap is each of the parts of the sphere determined by a secant plane.

Radius of a Sphere Formula

Area of a Spherical Cap

Area of a Spherical Cap Formula

Volume of a Spherical Cap


Volume of the Spherical Cap Formula


Example

Calculate the area and volume of the following spherical cap.

Spherical Cap

Hemisphere Exercise

Hemisphere Solution


Spherical Segment

Spherical Segment

A spherical segment is the part of the sphere between two parallel cutting planes.

The surface area of the spherical segment (excluding the bases) is called the zone.

Area of a Spherical Zone

Surface Area of the Zone Formula

Volume of the Spherical Segment

Volume of the Spherical Segment Formula


Example

Calculate the area of the zone and the volume of a spherical segment whose radius circles are 10 and 8 cm and the distance between them is 6 cm.

Spherical Segment and Zone

Hemisphere Exercise

Hemisphere Solution