12.7 surface area of spheres

12.7 Surface Area of Spheres

Objectives

Recognize and define basic properties 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.

• OB2=AB2+AO2 Pythagorean Theorem

• 102=AB2+32 Substitution• 100=AB2+9 Substitution• 91=AB2 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 r2

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

T=4 r2

T=4(3.14)64 T=803.8

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

10

T=1/2(4) 52+ 52

T=2*(3.14)*25+(3.14)*25 T=235.5

Assignment

• Pg. 674 #10-15, #17-24