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

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Automotive Technology (47.0604) T-Chart
Determine piston cubic inch displacement
=
Explain volume formulas and use them to solve problems
Program Task: Diagnose engine drivability problems.
PA Core Standard: CC.2.3.HS.A.12
Description: Explain volume formulas and use them to solve
problems.
Program Associated Vocabulary:
Math Associated Vocabulary:
STROKE, VOLUME, BORE, DISPLACEMENT
AREA, VOLUME, LENGTH, WIDTH, HEIGHT, RECTANGULAR,
ROUND, CYLINDRICAL, BASE, RADIUS, RECTANGULAR
PRISM
Program Formulas and Procedures:
Formulas and Procedures:
cu.in. displacement of a cylinder =
Volume:
2
bore π stroke
2
V = πr h
Cylinder:
CID =
or
V = πr
2
4
h
Piston bore (the diameter of the cylinder) squared times 3.14
(or π) times the stroke (the distance the piston travels up and
down) divided by 4. We divide by 4 because we squared the
diameter.
Cone:
1
πr
2
V =
/
h
3
Rectangular Prism:
V = lwh
Sphere:
4
πr
3
V =
/
3
Pyramid:
1
V =
/
(area of the base)h
3
h = height
b = base
l
= slant length or slant height
Example:
Bore = 5, Stroke = 10
How many cubic inches of air can a beach ball hold if it has a diameter
of 14 inches? Round to the nearest whole number.
2
bore πstroke
ci. in. =
Steps to finding volume:
4
1.
Identify the solid. (sphere)
2
5 π10
2.
Write the formula for calculating the volume of that solid using
ci. in. =
the formula sheet.
4
4
πr
3
ci. in. = 25× π ×10 ÷ 4
V =
/
3
3.
Identify what information you are given in the example.
3
3
ci. in. = 196.3495 in. (196.4 in. rounded)
Given: diameter (d) = 14”
4.
Solve for radius using the formula radius (r) = ½ (diameter).
r = ½ x 14 = 7
5.
Perform the necessary mathematical operations to obtain your
answer.
4
πr
3
4
3
3
V =
/
=
/
(3.14)(7
) = 1,436 in
3
3
6.
Write the appropriate unit after your answer.
3
1,436 in
Originated June 2011
CC.2.3.HS.A.12
Reviewed June 2015
1

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