The diameter and height of a cylinder are measured by a meter scale to be 12.6 ± 0.1 cm and 34.2 ± 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures?

The diameter of the cylinder is given as 12.6 ± 0.1 cm. Therefore, the radius is 6.3 ± 0.05 cm.
The height of the cylinder is given as 34.2 ± 0.1 cm.
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.
Substituting the values, we get:
V = π(6.3 ± 0.05)²(34.2 ± 0.1)
V = π(39.69 ± 0.63 ± 0.0025)(34.2 ± 0.1)
V ≈ π(39.69 ± 0.63)(34.2 ± 0.1)
To find the uncertainty in the volume, we can use the formula for the propagation of uncertainty:
ΔV/V = 2(Δr/r) + (Δh/h)
ΔV/V = 2(0.05/6.3) + (0.1/34.2)
ΔV/V ≈ 0.01587 + 0.00292 ≈ 0.01879
V ≈ π * 39.69 * 34.2 ≈ 4264 cm³
ΔV ≈ 0.01879 * 4264 ≈ 80 cm³
Therefore, the volume of the cylinder is approximately 4260 ± 80 cm³.
Thus the correct answer is option A which is 4260 ± 80 cm³.