12.7 Surface Area of Spheres
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Transcript of 12.7 Surface Area of Spheres
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12.7 Surface Area of Spheres
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Objectives
Recognize and define basic properties of spheres
Find surface areas of spheres
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Properties of Spheres
All properties of circles (things like chords diameters, radii, and tangents)
Can be thought like infinitely many congruent circles with same point for the center
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Great Circles
►The intersection of a plane and a sphere can be a point or a circle. When a plane intersects a sphere at the center, it is a Great Circle.
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Hemispheres• Each great circle separates the
sphere into two congruent halves called hemispheres.
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Example One• In the figure, O is the center, and plane R intersects the sphere in
circle A. If AO=3, and OB=10, find AB.
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• OB2=AB2+AO2 Pythagorean Theorem
• 102=AB2+32 Substitution• 100=AB2+9 Substitution• 91=AB2 Subtraction• 9.5=AB Square Root
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Surface Area of Spheres
If a sphere has a surface area of T square units and a radius of r units, then T=4 r2
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Example Two Find the surface area of sphere P with a radius of 8
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T=4 r2
T=4(3.14)64 T=803.8
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Example Three Find the Surface area of Hemisphere Q given a diameter of
10
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T=1/2(4) 52+ 52
T=2*(3.14)*25+(3.14)*25 T=235.5
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Assignment
• Pg. 674 #10-15, #17-24