SOLUTION: The altitude of a zone is 2 cm and the radius of the sphere is 9 cm. Find the volume of the spherical sector whose base is the given zone.

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Question 1192308: The altitude of a zone is 2 cm and the radius of the sphere is 9 cm. Find the volume of the spherical sector whose base is the given zone.
Answer by CPhill(1959) About Me  (Show Source):
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**1. Understand the Spherical Sector**
* A spherical sector is a portion of a sphere that consists of a spherical cap (a portion of the sphere's surface) and a cone with its apex at the center of the sphere.
**2. Formula for the Volume of a Spherical Sector**
* The volume (V) of a spherical sector is given by:
V = (2/3) * π * R² * h
where:
* R is the radius of the sphere
* h is the altitude (height) of the zone
**3. Given Values**
* Radius of the sphere (R) = 9 cm
* Altitude of the zone (h) = 2 cm
**4. Calculate the Volume**
* V = (2/3) * π * (9 cm)² * 2 cm
* V = (2/3) * π * 81 cm² * 2 cm
* V = (324/3) * π cm³
* V = 108π cm³
**Therefore, the volume of the spherical sector is 108π cubic centimeters.**