Notes

Outline

Math Training Module Two Volume In this module we will expand on our knowledge of calculating area and learn to calculate the volume of the various shaped containers that are components of a water treatment system.

Basic Three Dimensional Shapes Rectangle Cylinder Pyramid or Prism Cone   ·  Sphere

Units of Measure - Volume Volumes are measured in cubic units. The English system of  volume measurement includes the following units: Cubic Inches Cubic Yards Cubic Feet Gallons The Metric system of volume measurement includes the following units: Cubic Centimeters Cubic Meters Liters

"Volume calculations are three dimensional" Volume calculations are three dimensional.  They involve three dimensions such as length, width and depth. For example when we multiply the linear unit feet times the linear unit feet times the linear unit feet we get the volume unit measurement of cubic feet. So the unit multiplication ft x ft x ft gives the answer ft  or  cu ft.

"An example in the Metric..." An example in the Metric system of measurement would be to multiply the linear unit meter times the linear unit meter times the linear unit meter for a result of m  or cu m.

Calculating the Volume of a Rectangular Vessel The formula to calculate the volume of a rectangle is: Volume = Length x Width x Depth Volume = (l) x (w) x (d)

Example Calculate the volume of a rectangular tank with a length of 25 feet, a width of 10 feet and a depth of 15 feet. Volume = (l) x (w) x (d) Volume = 25 ft x 10 ft x 15 ft Volume = 3,750 cubic feet

Practice Exercise 1.  Calculate the volume of a rectangular tank with a length of 50 feet, a width of 25 feet and a depth of 15 feet. 2.  Calculate the volume of a rectangular tank with a length of 30 meters, a width of 10 meters and a depth of 10 meters.

Calculating the Volume of a Cylinder The formula to calculate the volume of a cylinder is: Volume = Area of Circle x Depth           or    Volume = p x r   x d           p = 3.14

Example Calculate the volume of a cylinder with a radius of 5 feet and a depth of 15 feet. Volume = pr   x d Volume = 3.14 x (5 feet)  x 15 feet Volume = 3.14 x 25 ft  x 15 ft Volume = 1,178 cu ft

Practice Exercise 1.  Calculate the volume of a cylindrical storage tank with a radius of 10 feet and a depth of 30 feet. 2.  Calculate the volume of a cylindrical storage tank with a diameter of 10 feet and a depth of 30 feet.

Calculating the Volume of a Cone The formula for calculating the area of a cone is: Volume = pr   x  depth                         3 Notice:  The volume of a cone is one-third the volume of a cylinder.

Example Calculate the volume of a cone with a radius of 10 feet and a depth of 15 feet. Volume = pr    x  depth                         3 Volume = 3.14 x (10 ft)   x 15 ft                              3 Volume = 1,571 cu ft

Practice Exercise 1.  Calculate the volume of cone with a radius of 5 feet and a depth of 5 feet. 1.  Calculate the volume of cone with a diameter of 5 feet and a depth of 10 feet.

Calculating the Volume of a Triangle: The formula to calculate the volume of a triangular vessel or a trough is: Volume = Area of Triangle x Length of Trough or  Volume =  base x height  x length       2

Example Calculate the volume of a triangle with a base of 8 feet, a height of 5 feet and a length of 8 feet. Volume = base x height x length                           2 Volume = 8ft x 5 ft x 8ft                         2 Volume = 160 cu ft

Practice Exercise 1.  Calculate the volume of  a triangle with a base of 15 feet, a height of 10 feet and a length of 12 feet. 2.  Calculate the volume of  a triangle with a base of 20 feet, a height of 15 feet and a length of 10 feet.

Calculating the Volume of a Sphere The formula to calculate the volume of a sphere is: Volume = p x (diameter)                  6 Where p = 3.14

Example Calculate the volume of a sphere with a diameter of 15 feet. Volume = 3.14 x 15 ft                     6 Volume = 1,767 cu ft

Practice Exercise 1.  Calculate the volume of sphere with a diameter of 20 feet. 2.  Calculate the volume of sphere with a diameter of 12.5 feet.

Calculating the Surface Area of a Sphere The formula for calculating the surface area of a sphere is denoted by A  :           A  = p x D

Example Calculate the surface area of a sphere with a diameter of 8 feet.

Practice Exercise 1.  Calculate the surface area of a sphere with a diameter of 3 feet. 2.  Calculate the surface area of a sphere with a diameter of 6 feet.