The volume of the drill bit can be calculated using the formula for the volume of a cylinder, V = πr²h. The given diameter is 7.500 cm and the distance the piston moves is 3.250 cm. The volume of the drill bit is 143.6 cm³ with an uncertainty of ±0.003 cm³.
The volume of the drill bit can be calculated using the formula for the volume of a cylinder,
V = πr²h, where r is the radius and h is the height of the cylinder.
Since the drill bit has a circular cross section, we can use its diameter to calculate the radius.
The given diameter is 7.500 cm, so the radius is half of that, or 3.750 cm. The distance the piston moves is given as 3.250 cm.
Plugging these values into the formula, the volume of the drill bit is:
V = 3.142 × (3.750 cm)² × 3.250 cm = 143.6 cm³.
The uncertainty in this volume can be calculated by considering the uncertainties in the measurements. The diameter has an uncertainty of ±0.002 cm and the distance has an uncertainty of ±0.001 cm.
To determine the uncertainty in the volume, we can combine these uncertainties using the rules for addition and multiplication. Since both the diameter and distance are being squared in the formula, the uncertainties are also squared. The uncertainty in the volume is therefore:
Uncertainty in volume = 3.142 × (2 × 0.002 cm) × (2 × 0.001 cm) = 0.0158 cm³.
Therefore, the correct answer is (b) 143.6 ± 0.003 cm³.