Question

1. lin measured the diameter of a circle in two different directions. measuring vertically, she got 3.5 cm, and measuring horizontally, she got 3.6 cm. explain s possible reasons why these measurements differ.

Explanation:

• Measurement Error:
• Instrument Limitations: Measuring tools like rulers have limited precision. A ruler might have markings at every \(0.1\) cm, but when aligning the edges of the circle with the ruler's markings, it's easy to mis - align. For example, if the vertical measurement was made with the top of the circle just below a \(0.1\) cm mark and the horizontal measurement was made with the side of the circle just above a \(0.1\) cm mark.
• Human Error: When Lin measures, her eyes might not be perfectly perpendicular to the ruler in both cases. If she is looking at the ruler at an angle for one of the measurements (e.g., looking slightly down on the vertical measurement and slightly up on the horizontal measurement), parallax error can occur. Parallax error is the apparent shift in the position of an object when viewed from different angles.
• Non - Circular Shape (if applicable):
• If the object is not a perfect circle (for example, it could be an ellipse that looks like a circle at a quick glance), the vertical and horizontal “diameters” (which would actually be the major and minor axes of an ellipse) would have different lengths. But if we assume the object is supposed to be a circle, measurement error is the more likely reason.

Answer:

The measurements differ likely due to measurement error (including instrument limitations and human - induced parallax error). If the object is not a perfect circle (though assumed to be a circle in the problem context, but if there was a mis - identification), the vertical and horizontal “diameters” could be different as in the case of an ellipse (but measurement error is the primary explanation here).