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
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.
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.
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
C=2πr
2*3.14*11
C=69.08
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
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.
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.
It is a Pentogonal Pyramid. It is a polyhydron. The reason why is because it is enclosed by a polygon.
Real Life Example 1
Cylinder
Real Life Example 2
Cube
Real Life Example 3
Cylinder
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- the sum of the areas of its faces.
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
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
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 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
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
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.
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
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.
Cone- a solid with one circular base.
Volume- a measure of the amount of space it occupies.
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
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
V=1/3*B*h
V=1/3*50.24*12
V=200.96 cm cubed