Measuring devices with ____ inside diameter will result in smaller volume errors than a device with a ___ inside diameter.

Measuring devices with ____ inside diameter will result in smaller volume errors than a device with a ___ inside diameter.

• A. wider; narrower
• B. same; same
• C. narrower; wider
• D. round; square

Answer: (C)

Volume errors in measuring devices are tied to the cross-sectional area of the liquid column. Since V = πr²h, a fixed uncertainty in reading the height (Δh) leads to a volume error of ΔV = πr²Δh. A smaller radius (narrower inside diameter) means a smaller cross-sectional area, so the same height-reading error translates into a smaller volume error. Conversely, a wider inside diameter increases the cross-sectional area and amplifies the volume error. Therefore, a device with a narrower inside diameter will yield smaller volume errors than one with a wider inside diameter.

Volume errors in measuring devices are tied to the cross-sectional area of the liquid column. Since V = πr²h, a fixed uncertainty in reading the height (Δh) leads to a volume error of ΔV = πr²Δh. A smaller radius (narrower inside diameter) means a smaller cross-sectional area, so the same height-reading error translates into a smaller volume error. Conversely, a wider inside diameter increases the cross-sectional area and amplifies the volume error. Therefore, a device with a narrower inside diameter will yield smaller volume errors than one with a wider inside diameter.