Q61E - Chemistry (OpenStax)

Question

Soccer is played with a round ball having a circumference between 27 and 28 in. and a weight between 14 and 16 oz. What are these specifications in units of centimeters and grams?

Step-by-Step Solution

Answer

68-71cm, 400-450g.

Step 1: Common conversion factor:

Step 2: Unit conversion factor for inches to cm:

If there are two equivalent amounts that are symbolized in different measuring units in a ratio format, then it is called a unit conversion factor. For example, the lengths of 2.54 cm and 1 in. are equivalent (by definition). Hence the ratio can be used to calculate a unit conversion factor.

 

\(\frac{{2.54\,{\rm{cm}}}}{{1\,{\rm{in}}}}\) (2.54cm per 1 in).

Step 3: Unit conversion factor for oz to grams:

If there are two equivalent amounts that are symbolized in different measuring units in a ratio format, then it is called a unit conversion factor. The conversion factor of oz to grams is 28.34gms to 1 oz.

\(\frac{{28.34{\rm{gm}}}}{{1\,{\rm{oz}}}}\)(28.34g per 1 in)