Lesson 8 4 Surface Area Of A Sphere
-
Upload
christine-oliver -
Category
Education
-
view
5.393 -
download
3
Transcript of Lesson 8 4 Surface Area Of A Sphere
![Page 1: Lesson 8 4 Surface Area Of A Sphere](https://reader036.fdocuments.us/reader036/viewer/2022071815/55a959fe1a28abdc4d8b461f/html5/thumbnails/1.jpg)
Lesson 8-4 A Lesson 8-4 A Surface Area of Surface Area of
SpheresSpheres
![Page 2: Lesson 8 4 Surface Area Of A Sphere](https://reader036.fdocuments.us/reader036/viewer/2022071815/55a959fe1a28abdc4d8b461f/html5/thumbnails/2.jpg)
INTRODUCTION
Archimedes, a Greek mathematician, found out that the surface area of a sphere is the same as the curved surface area of a cylinder having the same diameter as the sphere and a height same length as the diameter.
Curved surface area of cylinder = 2prh = 2pr(2r) = 4pr2 Thus the surface area of a sphere with radius r = 4 pr2
NOTE: The value of p can never be known exactly, so surface areas of spheres cannot be calculated exactly. Common approximations for p are: 3.14, and 22/7.
![Page 3: Lesson 8 4 Surface Area Of A Sphere](https://reader036.fdocuments.us/reader036/viewer/2022071815/55a959fe1a28abdc4d8b461f/html5/thumbnails/3.jpg)
Sphere Facts
Notice these interesting things:
It is perfectly symmetrical
It has no edges or vertices
It is not a polyhedron
All points on the surface are the same distance from the center
Sphere Radius
Surface Area = 4 × π × r2
Volume = (4/3) × π × r3
![Page 4: Lesson 8 4 Surface Area Of A Sphere](https://reader036.fdocuments.us/reader036/viewer/2022071815/55a959fe1a28abdc4d8b461f/html5/thumbnails/4.jpg)
How do you solve problems involving the surface area of a
sphere?
![Page 5: Lesson 8 4 Surface Area Of A Sphere](https://reader036.fdocuments.us/reader036/viewer/2022071815/55a959fe1a28abdc4d8b461f/html5/thumbnails/5.jpg)
EXAMPLE 1
A solid sphere has a radius of 3m.
Calculate its surface area. (Take p = 22/7)
Surface area = 4 pr² = 4 x 22/7 x 3 x 3
= 113m²
![Page 6: Lesson 8 4 Surface Area Of A Sphere](https://reader036.fdocuments.us/reader036/viewer/2022071815/55a959fe1a28abdc4d8b461f/html5/thumbnails/6.jpg)
EXAMPLE 2
Find the radius of a sphere with a
Surface area of 64pm²
Surface area = 4 pr²
64p = 4pr²
16 = r² r=square root of 16
r = 4 cm
The radius is 4cm.