Geometry 19 March 2013Warm up: Warm up: Check your homework. Check your homework. For EACH PROBLEM: √ if correct. X if incorrect.For EACH PROBLEM: √ if correct. X if incorrect.Work with your group mates to find and correct any errors. Please use a different color. Give yourself a Grade.Give yourself a Grade.

HOMEWORK DUE TODAY:pg. 534: 5, 7, 11, 12 pg. 540: 9, 10pg. 534: 5, 7, 11, 12 pg. 540: 9, 10

Objective

• Students will explore the derivation of SA and Volume formulas and apply them to solve problems.

• Students will take notes, participate in whole class discussion and work with their group.

• HOMEWORK DUE FRIDAY March 22:PG. 572: 4, 6 – 11 (Find vol AND surface area); 14

Surface Area of Surface Area of Prisms and CylindersPrisms and Cylinders

In general,

SA = ASA = Abasesbases + A + Asidessides

Surface AreaSurface Areaconecone

r = radiusl = slant height

Volume of Volume of

prisms and cylinders prisms and cylinders

Area of the base x heightArea of the base x height

V = AV = Abasebase x H x HWant more info? Want more info?

http://math.about.com/od/formulas/ss/surfaceareavol_3.htmhttp://math.about.com/od/formulas/ss/surfaceareavol_3.htm

V = 1/3 AV = 1/3 Abasebase∙ H∙ H

3baseA H

V

How can we find the formulas for the volume and surface area

of a sphere??

How many hemispheres will it take to fill a How many hemispheres will it take to fill a cylinder if they both have the same radius and cylinder if they both have the same radius and

the height of the cylinder = 2r?the height of the cylinder = 2r?see http://www.youtube.com/watch?v=aLyQddyY8ik

Vsphere = 22

3r H

Vsphere = 2 32 4(2 )

3 3r r r

Volume of a sphereVolume of a sphere

34

3

rV

r

Steps: 1) cube the radius2) multiply by 3) multiply by 44) divide by 3

In your classwork:

What is the volume of a spherewith a radius of 6 cm?a. 288π cm3b. 72π cm3c. 144π cm3d. 24π cm3

Surface Area of a Spherealgebraic proof

see page 562http://www.youtube.com/watch?v=rUgw8aZo7F0&feature=related

Surface area of a sphereSurface area of a sphere

24S r4in

Steps: 1) square the radius2) multiply by 2) multiply by 4

practicePage 466: 1 – 8 Odd Tables: #9 Even Tables: #10page 559: 1 – 5

Be ready to share your work with the class.Debrief

What math did we do today?What is easy?What is still confusing?