# 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... Tom and Bob want to create a garden as present to their mom on Mother's Day. They need to find how much mulch they should buy and fill the space with. | ## The Information is... The space in the yard is a parallelogram and so when measured it is 7ft tall (h) and 5ft long (b). How many ft^2 of mulch is needed | ## How to Solve..Formula : A=b*h Situation : A=5*7 Answer : Tom and Jerry need to buy 35ft^2 |

## Real Life Situations...

## The Information is...

## Section 10.2 Areas of Circles

## Real Life Situations... A grandmother wants to make a pillow to match her grand daughter's bed sheets. She needs to know how much fabric to cut for the pillow. | ## The Information is... The pillow is going to be a circle the radius is 12in. | ## How to Solve...Formula : A=Pi*r^2 Situation : A=Pi*12^2 Answer : The grandma will need to cut 452in^2 of fabric. |

## Real Life Situations...

## Section 10.4 Surface Areas of Prisms and Cylinders

Cylinders : S=2B+Ch or 2Pir^2+2Pirh

Prisms : S=2B+Ph

## Real Life Situations... Marge and her friends are going to participate in a soda guessing challenge which requires painting over the label of the can (I know, like why not pour the soda into a glass, duh). | ## The Information... The radius of the can is 1.5in, the height is 5in, the circumference is 9in. | ## How to Solve...Formula : 2B+Ch or 2*Pi*r^2+9*5 Situation : 2*Pi*1.5^2+9*5 Answer : 60in^2 |

## Real Life Situations...

## 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 l = (sqr.rt)r^2+h^2 | Cones are much like cylinders in that both have a circular base and curved edges. |

## 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

## Section 10.6 Volumes of Prisms and Cylinders

Cylinder : B*h or Pi*r^2*h

## Real Life Situations.../The Information Is... Billy wants to know how much his toy trailer can hold. The base is a rectangle and is 5 by 8 in the height is 3in. | ## How to Solve...Formula : B*h Situation : 5*8*3 Answer : 120in^3 | ## Euler's Formula F+v-2=E F : Number of Faces on a 3D Figure v : Number of vertices on a 3D Figure. E : Number of Edges on a 3D Figure. |

## Real Life Situations.../The Information Is...

## Section 10.7 Volumes of Pyramids and Cones

Cone : 1/3*Pi*r*h

## Real Life Situations... Jimmy wants to know the amount of ice in his extra-extra large waffle cone. | ## The Inforamtion Is.. The cones radius is 5in and its height is 10in. | ## 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