# Hemisphere

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

### Surface Area of a Hemisphere

### Volume of a Hemisphere

#### Examples

The dome of a cathedral has a hemispherical form with a diameter of 50 m. If the restoration costs $300 per m^{2}, what is the total cost of the restoration?

15,707.96 · 300 = **$4,712,388.98**

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

## Spherical Wedge

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

### Volume of a Spherical Wedge

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

### Area of a Spherical Lune

## Spherical Cap

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

### Area of a Spherical Cap

### Volume of a Spherical Cap

#### Example

Calculate the area and volume of the following spherical cap.

## 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

### Volume of the Spherical Segment

#### 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.