Chapter 10
Lily C.
Vocabulary
- Area = A
- Base = b
- Height = h
- Radius = r
- Circumference = linear length around a circle = C
- Length of 2 or more shapes lengths added = P
- Surface Area = S Ex. Painting or wrapping around something
- Area of the base = B
- Slanted length = l
- Volume = V
- A pattern that when folded will create a solid / 3D figure = Net
Formulas
- Parallelogram/Rectangle : b*h
- Trapezoid : 1/2(b1+b2)h
- Circle : Pi*r^2
- Triangle : 1/2*b*h
- Cylinders : 2B+Ch or 2Pir^2+2Pirh
- Prisms : 2B+Ph
Pyramid : B+1/2*P*l
Cone : Pi*r^2+Pi*r*l
Sphere : 4*Pi*r^2
- Prism : B*h
- Cylinder : B*h or Pi*r^2*h
- Pyramid : 1/3*B*h
- Cone : 1/3*Pi*r*h
- Sphere : 4/3*Pi*r^3
Section 10.1 Areas of Parallelograms and Trapezoids
Parallelogram : A=b*h
Trapezoids : A=1/2(b1+b2)h
Real Life Situations...
The Information is...
How to Solve..
Formula : A=b*h
Situation : A=5*7
Answer : Tom and Jerry need to buy 35ft^2
Section 10.2 Areas of Circles
Real Life Situations...
The Information is...
How to Solve...
Formula : A=Pi*r^2
Situation : A=Pi*12^2
Answer : The grandma will need to cut 452in^2 of fabric.
Cones-Cylinders-Spheres
Prisms
Pyramids
Section 10.4 Surface Areas of Prisms and Cylinders
Cylinders : S=2B+Ch or 2Pir^2+2Pirh
Prisms : S=2B+Ph
Real Life Situations...
The Information...
How to Solve...
Formula : 2B+Ch or 2*Pi*r^2+9*5
Situation : 2*Pi*1.5^2+9*5
Answer : 60in^2
Section 10.5 Surface Areas of Pyramids and Cones
Pyramid : B+1/2*P*l
Cone : Pi*r^2+Pi*r*l
Real Life Situation.../The Information Is.../How to Solve...
A tourist wants to know the surface area of the top of his house so he can know how much wood to buy. The top is a rectangular pyramid b=20ft h=10ft P=50ft l=30ft
Formula : B+1/2*P*l Situation : 20*10+1/2+50*30
Answer : 150000ft^2
Looking For the Slant Height
Section 10.6 Volumes of Prisms and Cylinders
Cylinder : B*h or Pi*r^2*h
Real Life Situations.../The Information Is...
How to Solve...
Formula : B*h
Situation : 5*8*3
Answer : 120in^3
Euler's Formula
F : Number of Faces on a 3D Figure
v : Number of vertices on a 3D Figure.
E : Number of Edges on a 3D Figure.
Section 10.7 Volumes of Pyramids and Cones
Cone : 1/3*Pi*r*h
Real Life Situations...
The Inforamtion Is..
How to Solve...
Formula : 1/3*Pi*r*h
Situation : 1/3*Pi*5*10
Answer : the ice cream cone holds 52in^3 ice cream
Extended : Spheres
A Sphere is different than other 3D Figures because it is not formed by polyhedrons, but is formed every and any point from the center is the same length.
Surface Area = 4*Pi*r^2
Volume =4/3*Pi*r^3