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EEJ MAIN Physics QUESTION #7040
Question 1
The diameter and height of a cylinder are $12.6 \pm 0.1 \text{ cm}$ and $34.2 \pm 0.1 \text{ cm}$ respectively. Calculate its volume using appropriate significant figures.
  • $4264 \pm 81 \text{ cm}^3$
  • $4264.4 \pm 81.0 \text{ cm}^3$
  • $4260 \pm 80 \text{ cm}^3$✔️
  • $4300 \pm 80 \text{ cm}^3$
Correct Answer Explanation

Volume $V = \frac{\pi d^2 h}{4} = \frac{\pi \times 12.6^2 \times 34.2}{4} \approx 4262.2 \text{ cm}^3$.

Since inputs have 3 significant figures, $V \approx 4260 \text{ cm}^3$.

Error calculation: $\frac{\Delta V}{V} = 2\frac{\Delta d}{d} + \frac{\Delta h}{h}$

$\Delta V = 4260 \left( 2 \frac{0.1}{12.6} + \frac{0.1}{34.2} \right) \approx 4260 (0.01587 + 0.00292) \approx 80 \text{ cm}^3$.

Final value: $4260 \pm 80 \text{ cm}^3$.