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

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? <img src="https://www.superprof.co.uk/resources/wp-content/uploads/2019/06/86_2-15615376139968-4358.gif"     >                               15,707.96 · 300 = <strong>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

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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.

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.