The diameter of a U.S quarter is 24.26 millimeters. How long is a line of 37 quarters laid edge to edge?

Question

Wyatt Anderson · Accepted Answer

#color(magenta)( "Length of line of 37 quarters laid edge to edge " = 897.62 " mm"#

Diameter of one U S quarter # = 24.26 " mm"#

The total distance is equal to the number of quarters multiplied by the quarter's diameter when they are arranged edge to edge.

#:.color(magenta)( "Length of a line of 37 quarters laid edge to edge " = 37 * 24.26 = 897.62 " mm"#

Claire Akin · Answer

undefined To calculate the length of a line of 37 quarters laid edge to edge, you would multiply the diameter of a single quarter by the number of quarters and subtract the overlap.

First, calculate the total diameter of the quarters laid edge to edge:

$$ \text{Total diameter} = \text{diameter of a single quarter} \times (\text{number of quarters} - 1) $$

$$ \text{Total diameter} = 24.26 \, \text{mm} \times (37 - 1) $$

$$ \text{Total diameter} = 24.26 \, \text{mm} \times 36 $$

$$ \text{Total diameter} = 872.16 \, \text{mm} $$

However, this only accounts for the edges touching, so you need to add the diameter of one quarter for the overlap:

$$ \text{Total length} = 872.16 \, \text{mm} + 24.26 \, \text{mm} $$

$$ \text{Total length} = 896.42 \, \text{mm} $$

So, the total length of a line of 37 quarters laid edge to edge is 896.42 millimeters.