1. Table of Contents 34. Surface Area & Volume of Spheres

2. Surface Area & Volume of Spheres
Std – MM2G3 Understand properties of circles
Essential Question – What is the difference between surface area and volume?

3. Definitions
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.
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.
Diameter of a Sphere – a chord that goes through the center.

4. C is the center of the sphere.
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 E D

5. Surface Area of a Sphere
S = 4r2
(it takes 4 circles to cover a sphere)
Ex: Find the surface area of a sphere with a radius of 8 cm.
S = 4(8)2
S = 4(64)
S = 256 cm2

6. Example Find the radius of a sphere with surface area of 200 cm2
SA = 4(r)2
200 = 4(r)2
15.9 = (r)2
r = 3.99 cm

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

8. Ex: The circumference of a great circle of a sphere is 15. 5 m
Ex: The circumference of a great circle of a sphere is 15.5 m. What is the surface area of the sphere?
S = 4r2
S = 4(7.75)2
S = 4( )
S =  m2 Or
754.8 m2
C = 2r
15.5 = 2r
15.5 = 2r
7.75 m = r

9. Ex: Find the volume of a sphere with a radius of 3 ft.
V = 36 ft3 or ft3

10. Ex: Find the radius of a sphere with a volume of 2304  cm3 .
Example
Ex: Find the radius of a sphere with a volume of 2304  cm3 .

11. Assignment
Pg. 241: #2-16 all