spheres surface area and volume geometry regular program sy 2014-2015 sources: discovering geometry...

SPHERESSurface Area and Volume

Geometry Regular ProgramSY 2014-2015

Sources:

Discovering Geometry (2008) by Michael Serra

Geometry (2007) by Ron Larson

The Geometric Solids

SPHERE

HEMISPHERE: Half a sphere PLUS the circular base

The circle that encloses the base

is the GREAT CIRCLE.

If you were to slice a pingpong ball, where do you slice it to get the largest circular cross-

section?

If a plane cuts a sphere along the center, then the

plane contains the great circle.

Is the equator In a globe a great circle?

How do we obtain the Volume of a sphere?

https://www.youtube.com/watch?v=h4j8l3p22e8

Video 1

How do we obtain the Volume of a sphere?

https://www.youtube.com/watch?v=YNutS8eIhEs

Video 2

Volume of a Sphere

Volume of a sphere

with radius r

Example:

How do we obtain the Surface Area of a sphere?

https://www.youtube.com/watch?v=cAxHYFRx1Fs

Video 3

How do we obtain the Surface Area of a sphere?

Video 4

https://www.youtube.com/watch?v=xuPl_8o_j7k

How do we obtain the Surface Area of a sphere?

Surface Area of a Sphere

Surface Area of a sphere

with radius r

How many circle areas cover the

sphere?

Example:

Sphere

Surface AreaVolume

Given a sphere with radius r

Solve for the VOLUME and Surface Area:

Solve for the VOLUME and Surface Area:

Solve for the VOLUME and Surface Area:

Solve for the unknown and Surface Area:

Solve for the unknown:

Solve for the unknown:

Solve for the unknown: