**spherical sector**

**by**

Jeslie lim

kigia valbuena

denise yang

Jeslie lim

kigia valbuena

denise yang

Spherical sector

A solid generated by revolving a sector of a great circle about a diameter of that circle.

volume

volume

Total surface AREA

properties

Example problems

1/3 ZR

where:

Z is the area of zone base

R is the radius of the sphere

Since Z = 2 (pi) Rh

v = 2/3 (pi) R^2 h

Zone + Lateral area of bounding cones

2 (pi) Rh + (pi) aR + (pi) bR

[(pi)R] 2h + a + b

or

but for Spherical Cone, b=0; thus

[(pi)R] 2h + a

1. The Spherical Sector is bounded by a zone and one or two conical surfaces.

2. The Spherical Sector having only one conical surface is called a spherical cone, otherwise it is called open spherical sector.

3. The base of a Spherical Sector is its zone.

1. Find the volume of a spherical sector

cut out of a sphere whose surface

area is 400 (pi) in^2 if the altitude

of the zone base is 3 in.

2. Find the volume of the spherical sector

cut out of a sphere of radius 16 cm, if the

altitude of the zone is 6 cm.