Final answer:
To estimate the maximum error in the volume of the cylinder, use the linear approximation. Consider the maximum error in the radius and use the formula ΔV = π(2rΔr + Δr²)h. However, since the maximum error in the diameter is not given, the actual maximum error cannot be determined without more information.
Step-by-step explanation:
To estimate the maximum error in the volume of the cylinder, we can use the linear approximation. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height.
In this case, we are given the diameter, which is 2 m. The radius can be calculated by dividing the diameter by 2, so r = 2/2 = 1 m.
Using the linear approximation, we can estimate the maximum error in the volume by considering the maximum error in the radius. If the radius has a maximum error of Δr, then the maximum error in the volume can be approximated as ΔV = π(2rΔr + Δr²)h.
Since the maximum error in the diameter is not provided, we cannot determine the actual maximum error in the volume without more information.