Chapter 10
Mackenzie K
Chapter 1: Area of Parallelograms and Trapezoids
Parallelogram
Formula: A=b*h
Base: Is the length of any one of it sidesHeight: Perpendicular distance between the base and the opposite side.
Trapezoid
Base; 2 parallel sides
Height: The perpendicular distance between the bases.
Practice Problem
A=b*h
A=300*400 (Multiply base times height)
A=120,000 ft squared
Area of Circle Formula
50 = 3.14 * r (Subtract 3.14 and add it to 50)
46.86 = r^2 (square root each number)
6.85 = r
Circle
Diameter: The distance across the center of the circle
Radius: The distance between the center and any point on the circle.
Circumfrance of a Circle Formula
C= 3.14 * 2
C= 6.28
Practice Problem
A=πr^2
A= 3.14*25
A=78.5cm^2
Chapter 3 : Three-Dimensional Figures
Prism
Pyramid
Cylinder
Cone
Sphere
Practice Problem
Vocab
Solid: a 3-dimensional figure that encloses a part of space
Faces: The polygons that form a polyhedron
Edges: the segments where faces of a polyhedron meet.
Vertex: A point where 3 or more edges meet.
Chapter 4: Surface Areas of Prisms and Cylinders
Surface Area of a Prism
The Surface Area of a prism is the sum of twice the area of a base B and the product of the base's perimeter P and the height h
Surface Area of a Cylinder
The surface area of a cylinder is the sum of twice the area of a base B and the product of the base's circumference C and the height h
Surface Area of a Triangular Prism
S=2(1/2*b*h) + Ph
The surface area of a prism is the sum of twice the area of a base B and the product if the base's perimeter P and the height h.
Chapter 5: Surface Areas of Pyramids and Cones
Surface Area of a pyramid
The surface area of a regular pyramid is the sum of the area of the base B and 1/2 the product of the base perimeter P and the slant height L.
Surface Area of a Cone
The surface area of a cone is the sum of the area of the circular base with radius r and the product of π, the radius r of the base, ad the slant height L.
Practice Problem
S = πr^2 + πrL
S = 3.14*7^2 + 3.14*7*14
S = 153.86 + 307.72
S = 461.58in^2
Vocab
Circumference: the distance around the circle.
Diameter: the distance across the circle through the center.
Slant Height: the height of any face that is not the base of a regular pyramid
Chapter 6: Volumes of prisms and Cylinders
Volume of a Prism
The volume of a prism is the product of the area of the base B and the height h
Volume of a Cylinder
V = πr^2h
The volume of a cylinder is the product of the area of a base B and the h.
Practice Problem
Triangular: V=Bh Circular: V=πr^2h
V=1/2*4*5*8 V=3.14*5^2*5
V=80in^3 V=392.5in^3
Chapter 7: Volumes of Pyramids and Cones
Volume of a Pyramid
The volume V of a pyramid is 1/3 the product of the area of the base B and the height h.
Volume of a Cone
The volume of a cone V is 1/3 the product of the area of the base B and the height h.
Related to Cylinders
Practice Problem
Find the formula and input numbers for letters.
V= 1/3πr^2h
V=1/3^3.14*3^2*6
V=56.52ft^3
Formulas
Chapter 1
- Area of a Parallelogram: A=bh
- Area of a Trapezoid: A=1/2(b1 + b2)h
- Area of a Circle: A=πr^2
- Surface Area of a Prism: S=2B+Ph
- Surface Area of Cylinder: 2πr^2 + 2πrh
- Surface Area of Pyramid: S= B+1/2PL
- Surface Area of a Cone: S= πr^2 + πrL
- Volume of a Prism: V=Bh
- Volume of a Cylinder: V=πr^2h
- Volumes of a Pyramids: V=1/3Bh
- Volumes of a Cone: V=1/3πr^2h
- Area of a triangle: A= bh1/2