Geometric Solids 1 Spheres

2 A sphere is formed by revolving a circle about its diameter. In space, the set of all points that are a given distance from a given point, called the center. Definition:

Spheres and Circle Terminology 3 Radius: A segment whose endpoints are the center of the sphere and a point on the sphere. Chord: A segment whose endpoints are on the sphere. Diameter: A chord that contains the sphere’s center. Tangent: A line that intersects the sphere in exactly one point. Radius Chord Diameter Tangent

Surface Area & Volume of Sphere 4 Volume (V) = Surface Area (SA) = 4 π r 2 r Example:Find the surface area and volume of the sphere. 12 cm

Great Circle & Hemisphere Great Circle: For a given sphere, the intersection of the sphere and a plane that contains the center of the sphere. A geographic representation would be the equator. Hemisphere: One of the two parts into which a great circle separates a given sphere. Great Circle Hemisphere

Finding the Volume of a Hemisphere 6 Find the volume of the following solid (Hemisphere). 10 cm

Finding the Surface Area of a Hemisphere 7 Find the Surface Area of the following solid (Hemisphere). 10 cm

Example #1 8 The beach ball has a radius of 7 inches. Find the Surface Area of the ball. What if we wanted to fill the ball up with water? How would we determine how much water the ball could hold? Find the volume!.

Example #2 9

Example #2 Solution 10

Example #3  A solid metal right cylinder is melted and recast as a sphere. The radius of the cylinder was 4 and the height was 18. Find the volume and surface area of the sphere.  The volume will not change! Start there. 11

Example #3 continued  Since the Volume of the Cylinder is the same as the Volume of the Sphere, then 12