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Answer :
Final answer:
The decrease in gas volume when a car engine's piston compresses it is approximately 176 cm³. The uncertainty in this volume is approximately 0.12 cm³. Thus, the correct answer includes these values.
Explanation:
To answer the student’s question regarding the decrease in volume when a car engine compresses gas using a piston, we first need to determine the volume change as the piston moves. This can be found with the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height (or distance the piston moves).
The diameter of the piston is given as 7.500 cm, so the radius is half of this, 3.750 cm. The volume decreased is therefore π * (3.750 cm)^2 * 3.250 cm, which calculates to approximately 176 cm³, answering part (a) of the question.
For part (b), the uncertainty in this volume can be determined using the uncertainties given for the diameter (0.002 cm) and distance (0.001 cm). When calculating uncertainties in multiplication, we add the relative uncertainties together. This results in a total relative uncertainty, which is then used to find the absolute uncertainty in the volume.
After performing these calculations, we find the uncertainty to be approximately 0.12 cm³, leading us to the conclusion that the correct answer is option (b): (a) 176 cm³, (b) 0.12 cm³.
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