Math With Mr. Prazak

 

Chapter 8

Page history last edited by Bill Prazak 10 mos ago

"People are born to succeed, not fail." Henry David Thoreau

Chapter 8

Circles - Radius, Diameter, Circumference

Quadrilaterals

3D Solids

Surface Area

Volume of Irregular Objects

Volume of Prisms

Cylinder - Surface Area & Volume

Composite Solids - Surface Area & Volume

Test

 

 

 

 


 

 

Circle Center.ppt Click this link to see how to find the center of a circle. Use this PPT to help you

complete the homework sheet.

 

Circumference of a circle: C = pi times diameter.

 

pi equals 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510...

 

Image:Pi-unrolled-720.gif

 

3.1415926...

 


 

 

 

Area of Quadrilaterals.ppt Click this link to see how to calculate the area of a quadrilateral. Use this PPT to help you

complete the homework sheet.

 


 

Area Formulae

square = a 2

rectangle = ab

parallelogram = bh

trapezoid = h/2 (b1 + b2) Trapezoid Area

circle = pi r 2

ellipse = pi r1 r2

triangle = (1/2) b h

 


 

 

Volume Formulae

cube = a 3

rectangular prism = a b c

irregular prism = b h

cylinder = b h = pi r 2 h

pyramid = (1/3) b h

cone = (1/3) b h = 1/3 pi r 2 h

sphere = (4/3) pi r 3

ellipsoid = (4/3) pi r1 r2 r3

 


 

Image:Hexagonal prism.pngImage:Cylinder (geometry).pngImage:Red cylinder.pngImage:Cylinder comp.jpg

 

Image:Sphere-wireframe.png A = 4 pi r^2 ,

 

Square Pyramid The volume of a pyramid is V = frac{1}{3} Ah where A is the area of the base and h the height from the base to the apex.

 

 

A right circular cone and an oblique cone V = frac{1}{3} b h A =pi r^2 + pi r s, where s = sqrt{r^2 + h^2} is the slant height.

 


 

 

Cool!! Click any of these and control the shape with your cursor. From http://mathworld.wolfram.com .

 

surfacevolume
cone1/3pir^2h
conical frustum1/3pih(R_1^2+R_2^2+R_1R_2)
cubea^3
cylinderpir^2h
ellipsoid4/3piabc
oblate spheroid4/3pia^2c
prolate spheroid4/3pia^2c
pyramid1/3Ah
pyramidal frustum1/3h(A_1+A_2+sqrt(A_1A_2))
sphere4/3pir^3
spherical cap1/3pih^2(3r-h)
spherical sector2/3pir^2h
spherical segment1/6pih(3a^2+3b^2+h^2)
torus2pi^2Rr^2

 

 


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