11.6 Surface Area of Spheres Standards: 8.0 & 9.0

Definitions Sphere – the locus of points in space that are a given distance from a given point. (looks like a ball)Sphere – the locus of points in space that are a given distance from a given point. (looks like a ball) Center of a Sphere – the given point in the middle.Center of a Sphere – the given point in the middle. Radius of a Sphere – segment from the center to a point on the sphere.Radius of a Sphere – segment from the center to a point on the sphere. Chord of a Sphere – a segment whose endpoints are on the sphere.Chord of a Sphere – a segment whose endpoints are on the sphere. Diameter of a Sphere – a chord that goes through the center.Diameter of a Sphere – a chord that goes through the center.

Parts of a Sphere C is the center of the sphere. AB is a diameter. CB & AC are radii. DE & AB are chords. C A B D E

Thm – Surface Area of a Sphere S = 4  r 2 (it takes 4 circles to cover a sphere) Why isn’t there a lateral area formula? Because spheres have no bases! Ex: Find the surface area of a sphere with a diameter of 8 cm. S = 4  (4) 2 S = 4  (16) S = 64  cm 2

More Definitions Great Circle of a Sphere – the cross section of a sphere sliced by a plane through its center.Great Circle of a Sphere – the cross section of a sphere sliced by a plane through its center. Hemisphere – ½ of a sphere.Hemisphere – ½ of a sphere. ** Every great circle splits a sphere into 2 hemispheres.

Ex: The circumference of a great circle of a sphere is 15.5  m. What is the surface area of the sphere? C = 2  r 15.5  = 2  r 15.5 = 2r 7.75 m = r S = 4  r 2 S = 4  (7.75) 2 S = 4  ( ) S =  m 2 Or m 2

Find the Surface Area of a Sphere Find the surface area of the sphere. Round your answer to the nearest whole number. a. The radius is 8 in. 8 in.

Find the Surface Area of a Sphere Find the surface area of the sphere. Round your answer to the nearest whole number. b. The radius is 5 cm. 10 cm.

Volume of a Sphere Volume = radius C

Assignment