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Volume of a Cylinder and Linear Approximation

- The volume V of a cylinder is computed using the values 2 m for the diameter and 8.1 m for the height. Use the linear approximation to estimate the maximum error in?

User LeMiz
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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.

User Greggreg
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