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Automotive Technology (47.0604) T-Chart

Instructor’s Script – Comparing and Contrasting

Whether calculating piston volume or mathematical volume, the math concepts and the formulas used are very similar. Occasionally,

automotive texts describe volume formulas in terms of diameter (d) instead of radius (r). When this happens, π is often replaced with

V = πr h

0.7854, (which is the same as

): Cylinder volume:

= 0.7854dh

If the volume involves a circular or spherical shape (cylinder, sphere, cone), then π will be part of the calculation. The best way to use π

in your calculations is to use a π key on the calculator, if available. Otherwise, using 3.14 as an approximation is fine.

The mathematical formulas for volume indicate a certain type of orientation that may not match the application in question. For example,

h will designate height of a cylinder, but if the cylinder is horizontal, h will be the same as the length:

Both cylinders have same volume:

Radius = 2

Length = 4

Height = 4

V = πr h

Use this formula for question three on page

three:

Common Mistakes Made By Students:

Students may use an incorrect formula to solve a problem: To rectify these errors have the students correctly identify the type of

object they are dealing with and use the appropriate formula. Frequently two formulas may be needed for complex problems.

Most volume formulas need radius (r), not diameter (d): If you are given a diameter, halve it to get the radius before using the

formula. Example: Diameter is 10 inches; radius = 10 ÷ 2 = 5 inches

Using consistent units: If the problem asks for the answer in square feet instead of square inches, be sure to either convert your given

measurements into feet first (inches ÷ 12 = feet) or convert your cubic inch answer into cubic feet (sq. in. ÷ 1,728 = cu. ft.).

1 cubic foot is a box 12 inches by 12 inches by 12 inches, so the calculation to convert cubic inches to cubic feet (or vice versa)

must use 12 x 12 x 12 = 1,728 cu. in. per cu. ft.

1 cubic yard is a box 3 feet by 3 feet by 3 feet, so the conversion of cubic feet to cubic yards uses 27 cu. ft. per cu. yd.

CTE Teacher's Extended Discussion

Some of the automotive technology topics that require an understanding of volume as well as the ability to calculate volume in a variety of

scenarios would include (but would definitely not be limited to):

Volume of cylinders/combustion chamber

Volume/displacement (propane, butane, oxygen, acetylene, nitrogen, diesel, etc., differences between gas/liquid uses).

Tubing and piping systems (AC suction and liquid lines)

Coolant systems (calculating anti-freeze temperature/pressure relationships within closed loop systems).

How many examples can you add?

Originated June 2011

CC.2.3.HS.A.12

Reviewed June 2015

Automotive Technology Chart With Answers - Engine Drivability Problems - Pennsylvania Department Of Education Page 2