3 D Summary and Formula Sheet

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MYP Geometry, 3-D Object Summary
Surface Area is about COVERAGE; the Area of All Surfaces. Volume is about SPACE. How much it takes to fill.
STEPS: 1) Identify Object, 2) Identify Formula, 3) SOLVE FOR MISSING PARTS***, 4) Plug and Chug!
Object
Surface Area
SA = 4  2
Sphere
Volume
4 3

3
2
  =  3
=
 SA = 3  2
 Hemisphere
Cylinder
Prism
Cone
3
SA = 2B + LA
SA =  + 
SA = 2B + Ph
V = Bh
V =  2 ℎ
V = Bh
SA = B + LA
SA =  + 
V = 

1
 =  2 ℎ
3

Pyramid
SA = B + LA
SA = B + ½ Pl
Variables:
LA = Lateral Area
h = height of the OBJECT
l = slant height
SA = Total Surface Area
r = radius
B = AREA of the BASE

V = 

V = Volume
P = Perimeter of the BASE
***Solving for missing parts may include many of the following previously learned formulas and skills***
Shape
Parallelogram:
Triangle:
Trapezoid:
Rhombus:
Circle:
Regular Polygon:
b = base h = height
Area Formula
A=b●h
A=½b●h
A = ½ (b1+b2) ● h
A = ½ (d1 ● d2)
A =  ∙ 2
A=½P●a
Variables:
d = diagonal r = radius P = perimeter
Pythagorean Theorem
c2 = a2 + b2
Soh Cah Toa
sin Ɵ = o/h
cos Ɵ = a/h
tan Ɵ = o/a
a = apothem
30-60-90
45-45-90
n – n √3 – 2n
n – n - n√2
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