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Surface Areas of Spheres

Learn about the fundamental properties of spheres and how to calculate their surface areas. Explore examples and key concepts such as hemispheres and great circles. Practice finding surface areas using real-life scenarios like baseballs.

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Surface Areas of Spheres

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  1. Surface Areas of Spheres • Recognize and define the basic properties of speres. • Find surface areas of spheres. Scenes such as reflective spheres over a checkerboard plane can be generated using computer ray-tracing.

  2. PROPERTIES OF SPHERES • A segment with endpoints that are the center of the sphere and on the sphere is a radius of the sphere. • A chord of the sphere is a segment with endpoints that are on the sphere. • A chord that contains the center of the sphere is a diameter of the sphere. • A tangent to a sphere is a line that intersects the sphere in exactly one point.

  3. PROPERTIES OF SPHERES Hemisphere Great Circle

  4. Key ConceptSurface Area of a Sphere If a sphere has a surface area of T square units and a radius of r units, then T = 4r2 r

  5. Example 1Surface Area Find the surface area of the sphere given the area of the great circle. A  201.1 in2

  6. Example 2Surface Area Find the surface area of the hemisphere. 4.2 cm

  7. Example 3Surface Area BASEBALL Find the surface area of a baseball with a circumference of 9 inches to determine how much leather is needed to cover the ball.

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