Using Mathematics Skills

Lesson 2

Determining Area and Volume

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.

Agriculture, Food and Natural Resources Standards Addressed!

PST.04.02. 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.04.02.01.a. Summarize and categorize the information needed to complete a bill of materials and cost estimate for an AFNR structure.

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?

Student Objectives

Describe the methods used to calculate the area of various shapesIdentify the application of determining areas and distancesDescribe the methods used to calculate the volume of various shapesIdentify the applications of determining volume in agriculture

Terms

AreaCircleEquilateral Isosceles TriangleLengthParallelogramRectangle

Right Triangle

Square

Scalene Triangle

Trapezoid

Triangle

Volume

Width

Area

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

How big is an Acre?

A little larger than a football field!

Determining the Area of a Square

Determining the Area of a Rectangle

If width = 1,000 ft

length = 2,000 ft

1,000 x 2000 ft = 20,000 ft2

Determining the Area of a Triangle

Kinds of Triangles

Determining the Area of a Triangle

If base = 600 ft.

and height = 750 ft.

area = 600 x 700 2

area = 210,000 ft2

area = 4.82 acres

Determining the Area of a Trapezoid

Determining the Area of a Trapezoid

Base 1 = 2000 ft.

Base 2 = 3000 ft.

Height = 1500 ft.

2000 + 3000 x 1500

2

area = 3,750,000 ft2

area = 86 acres

Determining the area of a Parallelogram

Determining the area of a Parallelogram

Base = 400 ft

Height = 600 ft

Area = 240,000 ft2

Determining the Area of a Circle

Determining the Area of a Circle

Radius = 25 ft.

252 x 3.14 = 1962.5 ft2

Volume

3 Dimensional

in “cubic” units

Important to remember - when converting from cubic feet to cubic

yard, divide by 27

Determining Cubic Area

Determining Cubic Area

Length = 100 ft

Width = 20 ft

Height = 20 ft

Volume = 40,000 ft3

Determining the Volume of a Cylinder

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 = 282.6 ft3

Determining the Area of a Cone

Determining the Area of a Cone

Radius = 10 ft

Height = 20 ft

102 x 3.14 x 20

3

Volume = 209,333 ft3

Determining the Area of a Sphere

Determining the Area of a Sphere

Diameter = 6 feet

3.14/6 x 63 =

112.968 ft3

The End!