Question

problems 3–4: the table shows the diameters of 4 different coins.

1. to determine how much metal is on one face of a coin, it is more useful to use the area rather than the circumference. explain why this is the case.

coin	diameter (cm)	area (sq. cm)
nickel	2.1
dime	1.8
quarter	2.4

Explanation:

The amount of metal on one face of a coin corresponds to the 2-dimensional surface coverage of that face. Circumference only measures the linear length of the coin's outer edge, which does not represent the surface area of metal. Area directly quantifies the total 2-dimensional space the metal occupies on the coin's face, so it is the relevant measurement for this purpose.

Answer:

Circumference only measures the coin's outer edge length, while area directly quantifies the total 2-dimensional surface of metal on the coin's face, making it the appropriate measure for the amount of metal on one face.