Question

The front wheel of a high-wheel bicycle from the late 1800s was larger than the rear wheel to increase the bicycle’s overall speed. The front wheel measured in height up to 60 in. Find the front wheel circumference and area of a high-wheel bicycle with a 60 in. front wheel..

Answer 1

The applicable formulas for the circumference (C) and area (A) of a circle with diameter d are ...

$\displaystyle C=\pi d\\\\A=\frac{\pi}{4}d^2$

Filling in the given vaue for d, we have

$C=\pi(60\, in)=60\pi \, in\approx 188.5\, in\qquad\mbox{circumference}\\\\A=\dfrac{\pi}{4}(60\, in)^{2}=900\pi\, in^{2}\approx 2827.4\, in^{2}\qquad\mbox{area}$