12.7 Surface Area of Spheres

Objectives Recognize and define basic properties of spheres Recognize and define basic properties of spheres Find surface areas of spheres Find surface areas of spheres

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

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.

Hemispheres Each great circle separates the sphere into two congruent halves called hemispheres.

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.

OB 2 =AB 2 +AO 2 Pythagorean Theorem 10 2 =AB Substitution 100=AB 2 +9 Substitution 91=AB 2 Subtraction 9.5=AB Square Root

Surface Area of Spheres  If a sphere has a surface area of T square units and a radius of r units, then T=4 r 2

Example Two  Find the surface area of sphere P with a radius of 8

T=4 r 2 T=4 r 2 T=4(3.14)64 T=4(3.14)64 T=803.8 T=803.8

Example Three Find the Surface area of Hemisphere Q given a diameter of 10 Find the Surface area of Hemisphere Q given a diameter of 10

T=1/2(4) T=2*(3.14)*25+(3.14)*25 T=235.5

Assignment Pg. 674 #10-15, #17-24