Chapter 10
Amanda B
Section 1
Formulas
Area of a Parallelogram: A= b*h
Area of a Trapezoid: A= 1/2(b1 + b2)h
Key:
A=Area
b= base of the shape
h= height of the shape
Area of a Trapezoid
Real Life Scenario
You are building a garden and you want it in a shape of a trapezoid. You need to find out how big you can make so that it fits in the amount of space you have in your yard. You will have to take measurements for the size of your yard, then use the formula for area of a trapezoid to find the biggest size that will fit in your yard.
Section 2
Vocabulary
Diameter: A line that crosses through the middle of a circle. The two end points of the line touch the edge of the circle
Radius: A line that goes to the middle of the circle, and reaches a midpoint.
Circumference: The distance around a circle. (the perimeter of a circle)
Circumference
C= pi times diameter or 2pi times radius.
Key:
Pi= 3.14...
d= diameter
r= radius
Real Life Scenario
You have a job at a school to paint a circle for the playground. The school also wants you to mark the radius with a large dot. They tell you they want the diameter to be 8 feet. You will find the circumference by using the formula pi times diameter. You also know that the radius is 1/2 of the diameter.
Section 3
Vocabulary
Polyhedron: A solid that is enclosed by polygons, and has only flat surfaces.
Prism: A polyhedron that has two congruent bases that lie in parallel planes.
Pyramid: A polyhedron with one base. All the other faces are triangles.
Cylinder: A solid with two congruent circular bases.
Sphere: A 3-D circle. Like a ball.
Cone: A solid that has a circular base, and it comes to a vertex.
Vertex: When two or more edges meet and form a point.
Edge: Where two faces meet.
Face: A side of the solid.
Real Life Scenario
You work for a company that makes soup cans. They tell you they want the can in a shape of a cylinder. This lesson would help you understand what a cylinder, and other three-dimensional shapes are.
Section 4
Formulas
Surface Area of a Prism: S= 2B+Ph
Key:
B = the area of the base
P = the perimeter of the base
h = the height of the prism
Surface Area of a Cylinder: S= 2*pi*r squared + 2*pi*r*h
Key:
r = the radius
h = height
Key:
B = the area of the base
P = the perimeter of the base
h = the height of the prism
Surface Area of a Cylinder: S= 2*pi*r squared + 2*pi*r*h
Key:
r = the radius
h = height
Vocabulary
Net: A two-dimensional pattern that forms a solid when it is folded
Surface Area: The sum of the areas faces
Surface Area: The sum of the areas faces
Real Life Scenario
You are designing as cereal box, and you need to find to total surface area so you know how big to put on all the details. You will have to use the formula for the surface area of a prism. You will then take those measurements and decide how big you want the advertisements.
Section 5
Formulas
Surface Area of a Pyramid: S= B+1/2 Pl
Key:
B= the area of the base
P= Perimeter of the base
l= The slant height
Surface Area of a Cone: S= pi*r squared + pi*r*l
Key:
r=radius
l=slant height
Key:
B= the area of the base
P= Perimeter of the base
l= The slant height
Surface Area of a Cone: S= pi*r squared + pi*r*l
Key:
r=radius
l=slant height
Vocabulary
Slant Height: The height of a face
Real Life Scenario
You are determined to find the surface area of a cone. You need to know the most possible cones you can stack, but they have to fit in the box the cones come in.
Section 6
Formulas
Volume of a Prism: V=B*h
Key:
B=area of the base
h=height
Volume of a Cylinder: B*h
Key:
B=are of the base= pi*r squared*h
Key:
B=area of the base
h=height
Volume of a Cylinder: B*h
Key:
B=are of the base= pi*r squared*h
Vocabulary
Volume: the amount of space an object takes up in a place
Real Life Scenario
You are designing a tissue box. The company says they want the box to hold 100 tissues. They give you the dimensions of each tissue. You have to come up with the volume of the box.
Section 7
Formulas
Volume of a Pyramid: V=1/3*B*h
Key:
B= area of the base
h= height
Volume of a Cone: V=1/3*B*h= 1/3 pi*r squared*h
Key:
B= area of the base
h= height
Volume of a Cone: V=1/3*B*h= 1/3 pi*r squared*h
Real Life Scenario
You work at an ice cream stand. There are three different sizes of cones. You need to know the volume of the cones so you can find out how many scoops of ice cream fit in each cone.
Volume of a Sphere
V=4/3*pi*r to the third
Volume of a Sphere
All Formulas
Area of a Parallelogram: A=b*h
Area of a Trapezoid: A= 1/2(b1+b2)*h
Area of a Circle: A= pi*r squared
Surface Area of a Prism: S= 2B+Ph
Surface Area of a Cylinder: S= 2*pi*r squared + 2*pi*r*h
Surface Area of a Pyramid: S= B+1/2 Pl
Surface Area of a Cone: S= pi* r squared+ pi*r*l
Volume of a Prism: V= B*h
Volume of a Cylinder: V= pi*r squared*h
Volume of a Pyramid: V= 1/3 B*h
Volume of a Cone: V=1/3* B*h
Volume of a Sphere: V= 4/3 pi*r to the third
Area of a Trapezoid: A= 1/2(b1+b2)*h
Area of a Circle: A= pi*r squared
Surface Area of a Prism: S= 2B+Ph
Surface Area of a Cylinder: S= 2*pi*r squared + 2*pi*r*h
Surface Area of a Pyramid: S= B+1/2 Pl
Surface Area of a Cone: S= pi* r squared+ pi*r*l
Volume of a Prism: V= B*h
Volume of a Cylinder: V= pi*r squared*h
Volume of a Pyramid: V= 1/3 B*h
Volume of a Cone: V=1/3* B*h
Volume of a Sphere: V= 4/3 pi*r to the third