Chapter 10
Riley W
Video of Formulas
2-d and 3-d shapes
Pictures of 2d and 3d shapes
Difference between 2d and 3d shapes
Another picture of 2d and 3d shapes
Chapter 10 section 1
Area of a trapezoid
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
7*5=35-------------answer to practice problem
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
Chapter 10 section 2
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
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
Chapter 10 section 4
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.
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
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.
Chapter 10 section 6
Volume: the amount of space a shape occupies
Volume of a prism
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
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
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
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.
The great pyramids of Giza
Anthropologist
Formula for volume of a pyramid
Volume of a cone
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
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 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