Question

I do not understand how to do this please help me I will appreciate it thx

Answer 1

One complete rotation, uses up the whole circumference, and the longer the diameter, the longer the circumference.

for a bike wheel, the longer the circumference or its perimeter, the more it goes, since the tire is longer.  A 27in tire will cover more ground in one-go-around than a 25in tire.

let's just check how much ground each one cover, and get their difference.

$\bf \stackrel{perimeter}{circumference}\textit{ of a circle}\\\\ C=\pi d\quad \begin{cases} d=diameter\\ -------\\ d=27 \end{cases}\implies C=\pi (27)\implies C=\stackrel{inches}{27\pi } \\\\\\ \stackrel{perimeter}{circumference}\textit{ of a circle}\\\\ C=\pi d\quad \begin{cases} d=diameter\\ -------\\ d=25 \end{cases}\implies C=\pi (25)\implies C=\stackrel{inches}{25\pi }\\\\ -------------------------------\\\\ 27\pi - 25\pi = \boxed{2\pi }\qquad \qquad \approx 6.2831853$