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 𝜋𝑟 2
Sphere
Volume
4 3
𝜋𝑟
3
2
 𝑉 = 𝜋𝑟 3
𝑉=
 SA = 3 𝜋𝑟 2
 Hemisphere
Cylinder
Prism
Cone
3
SA = 2B + LA
SA = 𝟐𝝅𝒓𝟐 + 𝟐𝝅𝒓𝒉
SA = 2B + Ph
V = Bh
V = 𝜋𝑟 2 ℎ
V = Bh
SA = B + LA
SA = 𝝅𝒓𝟐 + 𝝅𝒓𝒍
V = 𝑩𝒉
𝟑
1
𝑉 = 𝜋𝑟 2 ℎ
3
𝟏
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
𝟏
V = 𝑩𝒉
𝟑
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 = 𝜋 ∙ 𝑟2
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