This document defines and provides formulas for calculating the area and volume of common geometric shapes. It includes: - Formulas for calculating the area of squares, rectangles, triangles, circles using measurements of sides, bases, heights, and radii. Area is measured in square units. - Formulas for calculating the volume of cubes, boxes, spheres, cylinders, and cones using measurements of sides, lengths, widths, heights, radii, and formulas involving pi. Volume is measured in cubic units. - Examples applying each formula to sample measurements to calculate the actual area or volume value.

1. Review of Area and Volume Image from Flickruser toastforbrekkie on Feb 12th, 2009 http://www.flickr.com/photos/toastforbrekkie/3275037811/

3. Two-dimensional objects only

4. Square Units

5. Three dimensional space in an object

6. Three-dimensional objects only

8. Area of a Square A=S2 Area of a square is equal to the side squared Units: Unit of Side2 S Ex: S=2 in A=S2 A=2*2 A=4in2 Ex: S=7.4 ft A=S2 A=7.4*7.4 A=54.76 ft2 S

9. Area of a Rectangle A=S1*S2 Area of rectangle is equal to Side 1*Side 2 Units=unit of side2 S1 S2 Ex: S1=3 S2=5 A=S1*S2 A=3*5 A=15 units2 Ex: S1=15.6 cm S2=23.1 cm A=S1*S2 A=15.6*23.1 A=360.36 cm2

10. Area of a Triangle A=1/2b*h Area of the triangle equals one half of the base times the height Units: units of b and h2 h b Ex: b=4 h=3 A=1/2b*h A=1/2(4)*3 A=6 units2 Ex: b=5.6ft h=7.4ft A=1/2b*h A=1/2(5.6)*7.4 A=20.72 ft2

11. Area of a Circle A=πr2 Area of a circle is equal to pi (3.14159) times the radius2 Units= units of r2 r Ex: r=2 A= πr2 A= π(2)2 A=12.566 units2 Ex: r=57.2 cm A= πr2 A= π(57.2)2 A=10278.78 cm2

12. Volume of a Cube V=S3 Volume of a cube is equal to the side cubed Units= unit of side3 S S Ex: S=3.5 ft V=S3 V=3.53 V=42.875 ft3 S Ex: S=7in V=S3 V=73 V=343 in3

13. Volume of a Box V=l*w*h Volume of a box equals the length times the width times the height Units= units of l,w,h3 w l h Ex: l=3 w=7 h=2 V=l*w*h V=3*7*2 V=42 units3 Ex: l=2.3 w=4.7 h=3.1 V=l*w*h V=2.3*4.7*3.1 V=33.511 units3

14. Volume of a Sphere V=4/3πr3 Volume equals four thirds pi (3.14159) times the radius cubed Units= units of the radius3 r Ex: r=4.7 in V=4/3πr3 V=4/3π(4.7)3 V= 434.893 in3 Ex: r=2 V=4/3πr3 V=4/3π(2)3 V=33.51 units3

15. Volume of a Cylinder V= πr2 h Volume of a cylinder is equal to pi (3.14159) times the radius squared times the height Units= units of r,h3 r h Ex: r=1.6 h=3.4 V= πr2 h V= π(1.6)2 (3.4) V=27.344 units3 Ex: r=3 h=5 V= πr2 h V= π(3)2 (5) V=141.372 units3

16. Volume of a Cone V=1/3πr2 h Volume of a cone is equal to one third times pi (3.14159) times the radius squared times the height Units=unit of r,h3 h r Ex: r=4 h=5 V= 1/3πr2 h V= 1/3π(4)2 (5) V=83.776 units3 Ex: r=3.2 h=7.9 V= 1/3πr2 h V= 1/3π(3.2)2 (7.9) V=84.714 units3

17. The END