Chapter 10

Michael S.

Formula's

Area of a Parallelagram

A=b*h

Area of a Trapoziod

A=1/2(b+b)h

Area of a Circle

A=π*r*r

Surface Area of a Prism

S=2B+Ph

Surface Area of a Cylinder

S=2πr*r+2πrh

Surface Area of Pyramid

S=B+1/2*Plt

Surface Area of a Cone

S=πr*r+πrl

Surface Area of a Sphere

S=4πr*r

Volume of a Prism

V=Bh V=lwh

Volume of a Cylinder

V=Bh V=πr*rh

Volume of a Pyramid

V=1/3Bh

Volume of a Cone

V=1/3*Bh 1/3(πr*r)h

Volume of a Sphere

V=4/3*πr*r
Symbol meanings
B=Area of the base h=Hight
r=Radius w=Width
V=Volume l=Slant hight
P=Perimiter b=Base

Chapter 10/1 Areas of Parallelograms and Trapezoids

Vocabulary

Base of a Parallelogram- the length of any one of its sides.

Height of a Parallelogram- the perpendicular distance between the bases.

Bases of a trapezoid- Its two parallel sides.

Height of a trapezoid- the perpendicular distance between the bases.

Parallelogram Exampe

A=bh

A=10*5

A=50 inches square

Trapizoid Example

A=1/2(b+b)h

A=1/2(22+38)6

A=1/2*60*6

A=1/2*360

A=180 inches squared

Real Life Situation

You are measuring the area of your living room so you can get carpet. It is 15 ft across one way and 12 ft across the other way. You need the total area of the room.

A=b*h

A=12*15

A=180 ft sq

Chapter 10/2 Area of Circles

Vocabulary

Circle- the set of all points in a plane that are the same distance from a fixed point called the center.
Radius- the distance from the center to any point of the circle.
Diameter- the distance across the circle through the center.
Circumference- the distance around the circle/perimeter.

How to find circumference

r=11
C=2πr
2*3.14*11
C=69.08

Circle Example

A=πr*r
A=3.14*(8*8)
A=200.96

Real Life Situation

You are are planing on building a circular garden. You need to find an area that will fit the garden if the diameter is 10 ft. First you need to find the area the garden will take up. Find the area of the circle.
A=πr*r
A=3.14 *(5*5)
A=3.14*25
A=78.5

Chapter 10/3 Three-Dimensional Figures

Vocabulary

Solid- a three dimensional figure that encloses a part of space.
Polyhedron- a solid that is enclosed by polygons.
Faces- the polygons that form a polyhedron.
Prism- a polyhydron with two congruent bases that lie in parallel and the other rectangular faces.
Pyramid- a polyhydron with one base and triangular sides(faces).
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 a space that are the same distance from a fixed point called the center.
Edges- segments where the faces of a polyhedron meet.
Vertex- a point where three or more edges meet.

Three-Dimensional Figures Example

Classify the solid and tell whether it is a polyhydron. Explain why or why not:
It is a Pentogonal Pyramid. It is a polyhydron. The reason why is because it is enclosed by a polygon.

Chapter 10/4 Surface Areas of Cylinders and Prisms

Vocabulary

Net- a two-dimensional pattern that forms a solid whin folded.
Surface Area- the sum of the areas of its faces.

Surface Area of a Prism Example

S=2B+Ph
S=2*(8*3)+(22*4)
S=48+88
S=136 cm squared

Real Life Situation

You want to paint a board. You need to find out the surface area of the board, so you can figure out how much piant you need to buy. The boards hight is 4ft its length is 2ft its width is .5 ft.Find the surface area.
S=2B+Ph
S=2*1+5*4
S=2+20
S=22 ft squared

Surface Area of a Cylinder Example

S=2πr*r+2πrh=2B+Ch
S=(2*3.14*(5*5))+(2*3.14*5*15)
S=157+471
S=628 cm squared

Chapter 10/5 Surface Areas of Cones and Pyramids

Vocabulary

Slant Height- the hight of the lateral face, any face exept the base.

How to Find Slant Hight

First make the object two-dimensional. Then you can see the hight and the length of the base. Divide the base in half. You need to find the hypotenuse of the triangle that those two parts make. The hypotenuse is the slant height. You use the pathagorean therum a²+b²=c² to figure out the hypotenuse. The answer to that will give you the slant hight of a pyramid or cone.

Surface Area of a Pyramid Example

S=B+1/2Pl
S=(10*8)+1/2*36*7.2
S=80+129.6
S=209.6

Surface Area of a Cone Example

S=πr*r+πrl
S=3.14*8*8+3.14*8*21.54
S=200.96+541.0848
S=742.0448 units squared

Real Life Situation

You want to find the surface area of your ice cream cone. Find the surface area of a cone with an open base.
S=πr*r+πrl
S=π1*1+π1*6.08
S=3.14+19.09(take out B(area of the base))
S=19.09

Chapter 10/6 Volumes of Prisms and Cylinders

Vocabulary

Volume- a measure of the amount of space it occupies.

Volume of a Prism Example

V=Bh
V=(10*5)2
V=50*2
V=100 cm cubed

Volume of a Cylinder Example

V=π(r*r)*h
V=3.14*16*8
V=401.92 cm cubed

Real Life Situation

You want to fill in a wood pecker hole on your house. You need to find the volume of the cylinder shaped hole. The depth of the hole is 2 cm, the height of the hole is 4 cm. Find the volume of the wood that will be able to plug the hole.
V=π(r*r)*h
V=π(2*2)*2
V=π*4*2
V=25.12 cm cubed

Chapter 10/7 Volumes of Pyramids and Cones

Vocabulary

Pyramid- a polyhedron with one base and the other faces are triangles.
Cone- a solid with one circular base.
Volume- a measure of the amount of space it occupies.

Volume of a Pyramid Example

V=1/3Bh
V=1/3*(6*6)*4
V=1/3*36*4
V=48

Volume of a Cone Example

V=1/3*(π*r*r)*h
V=1/3*(3.14*25)*8.7
V=1/3*78.5*8.7
V=227.65 cm cubed

Real Life Situation

You want to find how much ice cream would fit in an ice cream cone if it fit the cone perfectly. The diameter of the cone is 4 cm and the height of the cone is 12 cm. Find the Volume of the cone.
V=1/3*B*h
V=1/3*50.24*12
V=200.96 cm cubed