Question

a circle has a radius of 5 feet. What is the circumference of a bigger circle if the scale factor of the smaller to bigger is 2:5

Answer 1

`\bf \cfrac{small~radius}{large~radius}\qquad 2:5\qquad \cfrac{2}{5}\qquad \cfrac{5}{x}=\cfrac{2}{5}\implies \cfrac{5\cdot 5}{2}=x\implies \cfrac{25}{2}=x\\\\ -------------------------------\\\\ \textit{circumference of a circle}\\\\ C=2\pi r\quad \begin{cases} r=radius\\ -----\\ r=(25)/(2) \end{cases}\implies C=\underline{2}\pi \cdot \cfrac{25}{\underline{2}}\implies C=25\pi`