# Chapter 10

## Video of Formulas

Volume and Surface Area formulas

## Area of a trapezoid

A=1/2(b1+b2)h---Area of a trapezoid Real Life: Imagine you and your wife are putting a new roof on your house due to a tornado, you now what the area of your house is but you need to find the accurate area for your new roof so it fits just right. Height=20 ft.

Base one=15ft.

Base two=16 ft.

1/2(b1+b2)H

1/2(15+16)20

1/2 *31*20

15.5*20

a=310 ft squared---------------answer to real life scenario

Practice Problem: Base one=6ft. Base two=8 ft. h=5 ft.

6+8=14

14/2=7

## Formula for a Parallelogram

A=b*h----Area of a parallelogram Real life: Your wife asks you to build a garden for her but not just any garden a parallelogram shaped garden. Formula for area: b*h h=6ft. b= 10ft. 6*10-------------------->area equals 60 ft. squared Practice Problem: b=8 h=13 8*13 area equals 104 ft. squared V

Vocabulary:

Base of a parallelogram: the length of any one of a parallelogram's sides

Height of a parallelogram: the height of any one of a parallelogram's sides

Bases of a trapezoid: the two parallel sides of a trapezoid

Height of a trapezoid: the perpendicular distance between the bases

Finding areas of parallelograms, triangles, trapezoids

## Area of a circle

Area=3.14*r squared--------------Area of a circle Real life: You are a designer for a tire company recently you were asked by the CEO to design a wheel that is the perfect size for any vehicle. r=13 in. 13*3.14=40.82---------------area of the tire.

Practice problem: d-------------diameter d=7in. 7*3.14=21.98

Vocabulary:

area: the amount of surface the figure covers

Circle: the set of all points in a plane that are the same distance from a fixed point

radius: the distance from the center to any point on the circle

Diameter: the distance across the circle through the center

Circumference: the distance around the circle Pi: a symbol for the constant 3.14

Area of a circle

## Chapter 10 section 3

Vocabulary:

Solid: a three dimensional figure that encloses a part of space

Polyhedron: a solid enclosed by polygons

Face: polygons that form a polyhedron

Prism: a polyhedron that has two congruent bases that lie in parallel planes

Pyramid: a polyhedron that has one base and the faces are triangles

Cylinder: A solid with two congruent circular bases that lie in parallel planes

Cone: a solid with one circular base

Sphere: a solid formed by all points in space that are the same distance from a fixed point called the center

## Surface area of a prism

B---------area of the base P=the perimeter of the base h= the height

Vocabulary:

Net: is a two-dimensional pattern that forms a solid when folded

Surface Area: the sum of the areas of the faces

Formula for surface area of a prism: S=2B=Ph

Real life scenario: You are designing a camper that is perfect for the average American family

The length of the base= 13 ft. The height of the base= 5 ft.

B= 65ft. 65*2 =130ft 13+13+5+5=36 ft.=P

130ft + 35ft*5

S=305 ft. squared

Practice Problem:

Length of base=5 height of base = 2 B=10ft.

2*10+Ph

20+14*2

S=48ft. squared

## Surface area of a cylinder

S=2B+Ch= 2*3.14*r squared + 2*3.14*r*h

Real life scenario: You are the CEO for a soda can producing company and you decide you want to give your consumers a bigger soda can for a little more price

r=0.6in h=4in.

2.26in. + 15.1

17.36in.

Practice equation:

r=5in. h=10in.

12.56 in+314

326.56 in.

Sec 12.2: Surface Area of Prisms and Cylinders

## Chapter 10 section 5

Vocabulary:

Slant height: the height of a lateral face all faces except the base

Formula to find the slant height square root the sum of h squared and r squared or the Pythagorean theorem

## Surface area of a Pyramid

S=B+1/2Pl l=the slant height P=perimeter of the base

Real life: Imagine you are an Egyptian building the great pyramids of Giza, you need to find the surface area.

B=200ft. + 1/2*100*150 P=100ft. l=150ft.

S=7,700ft. squPractice problem: B=10ft. P=8ft. l=9.5 ft.

10+1/2*8*9.5

S=48 ft. squared

## Surface area of a cone

S=3.14*r squared + 3.14*r*l

Real life: You want to find the surface area of a cone. r=.7 in. l=7 in.

.49*3.14+3.14*.7*7

1.54+15.4

S=16.926 in. squared

Practice problem:

r=7 in. h=20 in.

49 in. + 400 in.

l=449 in.

153.86 in. + 3.14*r*l

156.83 in. +9,869.02 in.

S=9,869.02 in.

12.3 Surface Area of Pyramids and Cones 2nd Part

## Chapter 10 section 6

Vocabulary:

Volume: the amount of space a shape occupies

## Volume of a prism

V=Bh B= area of the base

Real life: Imagine you are designer for Toyota and they want you to create a mini-van that is the right size for the average american family. B= 52 ft. h=4.5 ft.

V=52*4.5

V=234 ft.

Practice problem= B= 4 units h=2 units

V=8 units

## Volume of a cylinder

V=B*h B=3.14*r squared *h

Real life: You are the CEO of Coca cola and you have decided to make the soda cans bigger, you need to find the volume r=.7 in. h=4 in.

V= 3.14* 0.49*4

V=1.5386* 4

V=6.15 in. to the third power

Practice problem: B= 28 units h=40 in.

V=1,120 in.

## Chapter 10 section 7

Vocab.

Pyramid=a polyhedron with one, and the other faces are triangles

Cone=a solid with one circular base

Volume=the measure of the amount of space a solid occupies

## Volume of a pyramid

V=1/3*B*h

You are a anthropologist that is studying the great pyramids of Giza and you want to know the volume of the pyramids

l=200 ft. h=500 ft. B=100,000 ft.

100,000*500 ft.

50,000,000/3

V=16,666,666.666666666666666666666666666666666666666666666667 ft.

Practice problem: B=13 in. h= 16 in.

13*16

208/3

V=69.3333333333333333333333333333333333334 in.

## Volume of a cone

V=1/3*B*h=1/3*r squared*3.14*h

Real life: You want to find the volume of the ice cream cone your eating.

r=1 in. h= 5 in.

1*1=1

1*5=5

5*3.14= 15.7

15.7/3

V=5.233333333333333333333333333 in.

Practice Problem: B=3 in. h=6 in.

3*6

18/3

V=6

## Volume of a sphere

V=4/3*3.14*r squared*r

Real life: you want to find the volume of a sphere

r=6 in.

6*6=36*6

216*3.14

678.24*4/3

V=904.32 in.

Area of a parallelogram= b*h

Area of a trapezoid=1/2(b1+b2)h

----------------------------------------------10.1

Area of a circle= 3.14*r squared

-----------------------------------------------10.2

surface area of a prism =2*B(area of the base)+P(perimeter of base) *h

Surface area of a cylinder=2*B+C( circumference of base)*h

--------------------------------------------------------------------10.4

Surface area of a pyramid=B+1/2*P*l( slant height)

Surface area of a cone= 3.14* r squared +3.14*r*l

-------------------------------------------------------------------10.5

Volume of a prism=B*h

Volume of cylinder=3.14*r squared *h

-------------------------------------------------------10.6

Volume of a pyramid=1/3*B*h

Volume of a cone=1/3 *B*h

Volume of a sphere=4/3*3.14*r squared *r