1. Using Mathematics Skills

2. Determining Area and Volume
Lesson 2
Determining Area and Volume

3. Next Generation Science/Common Core Standards Addressed!
CCSS.Math.Content.8 .EE.A.4 - Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
CCSS.Math.Content.8.EE.B.5 - Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

4. Agriculture, Food and Natural Resources Standards Addressed!
PST Determine structural requirements, specifications and estimate costs for AFNR structures
Sample Measurement: The following sample measurement strands are provided to guide the development of measurable activities (at different levels of proficiency) to assess students’ attainment of knowledge and skills related to the above performance indicator. The topics represented by each strand are not all-encompassing.
PST a. Summarize and categorize the information needed to complete a bill of materials and cost estimate for an AFNR structure.

5. Bell Work
What are some agricultural occupations which might require math skills to determine area and volume?
What are some examples of problems common to these occupations
Have many of you have had to use mathematical skills to complete a job?

6. Student Objectives
Describe the methods used to calculate the area of various shapes
Identify the application of determining areas and distances
Describe the methods used to calculate the volume of various shapes
Identify the applications of determining volume in agriculture

7. Terms
Area
Circle
Equilateral
Isosceles Triangle
Length
Parallelogram
Rectangle
Right Triangle
Square
Scalene Triangle
Trapezoid
Triangle
Volume
Width

8. Area Defined as the measure of the amount of surface Two dimensional
Reported in Square inches, square feet, acres, square meters, etc.
To convert square feet to acres, divide by 43,560

9. How big is an Acre?
A little larger than a football field!

10. Determining the Area of a Square

11. Determining the Area of a Rectangle
If width = 1,000 ft
length = 2,000 ft
1,000 x 2000 ft = 20,000 ft2

13. Determining the Area of a Triangle

15. Kinds of Triangles

16. Determining the Area of a Triangle
If base = 600 ft.
and height = 750 ft.
area = 600 x
area = 210,000 ft2
area = 4.82 acres

17. Determining the Area of a Trapezoid

18. Determining the Area of a Trapezoid
Base 1 = 2000 ft.
Base 2 = 3000 ft.
Height = 1500 ft.
x 1500 2
area = 3,750,000 ft2
area = 86 acres

19. Determining the area of a Parallelogram

20. Determining the area of a Parallelogram
Base = 400 ft
Height = 600 ft
Area = 240,000 ft2

21. Determining the Area of a Circle

22. Determining the Area of a Circle
Radius = 25 ft.
252 x 3.14 = ft2

23. Volume 3 Dimensional in “cubic” units
Important to remember - when converting from cubic feet to cubic yard, divide by 27

24. Determining Cubic Area

25. Determining Cubic Area
Length = 100 ft
Width = 20 ft
Height = 20 ft
Volume = 40,000 ft3

26. Determining the Volume of a Cylinder

27. Determining the Volume of a Cylinder
If height = 10 feet
and radius is 3 feet
what is the volume of this cylinder?
32 x 3.14 x 10 = ft3

28. Determining the Area of a Cone

29. Determining the Area of a Cone
Radius = 10 ft
Height = 20 ft
102 x 3.14 x
Volume = 209,333 ft3

30. Determining the Area of a Sphere

31. Determining the Area of a Sphere
Diameter = 6 feet
3.14/6 x 63 = ft3

32. The End!