Question
11) The ideal diameter of a piston for one type of car is 108 mm . The actual diameter vary from the ideal at most 0.0012 mm . find the range of acceptable diameter of the piston.
Ask by King Parry. in Ethiopia
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The acceptable diameter range for the piston is from 107.9988 mm to 108.0012 mm.
Solution
1. Let the ideal diameter be given by
\[
d = 108 \text{ mm}
\]
2. The piston’s actual diameter can vary by at most
\[
\pm 0.0012 \text{ mm}
\]
3. Therefore, the acceptable range of the diameter is from
\[
108 - 0.0012 \text{ mm}
\]
to
\[
108 + 0.0012 \text{ mm}
\]
4. Calculating the limits:
\[
\text{Lower limit} = 108 - 0.0012 = 107.9988 \text{ mm}
\]
\[
\text{Upper limit} = 108 + 0.0012 = 108.0012 \text{ mm}
\]
5. Thus, the range of acceptable diameters is
\[
107.9988 \leq d \leq 108.0012 \text{ mm}
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To find the range of acceptable diameters for the piston, you start with the ideal diameter of 108 mm and consider the maximum allowable variation of 0.0012 mm. So, you subtract and add this variance to the ideal diameter. The minimum acceptable diameter would be: 108 mm - 0.0012 mm = 107.9988 mm. The maximum acceptable diameter would be: 108 mm + 0.0012 mm = 108.0012 mm. Therefore, the acceptable range of the piston diameter is from 107.9988 mm to 108.0012 mm. Now you can ensure that the pistons fit perfectly into the engine, maintaining optimal performance and longevity!
