Question

a small silver dollar pancake served at the restaurant has a circumference of 2 inches.A regular pancake has a circumference of 4 inches.Is the area of the regular pancake twice the area of the river dollar pancake?Explain.

Answer 1

`\bf \textit{circumference of a circle}\\\\ C=2\pi r\quad \begin{cases} r=radius\\ -----\\ C=2 \end{cases}\implies 2=2\pi r\implies \cfrac{2}{2\pi }=r\implies \cfrac{1}{\pi }=r \\\\\\ \textit{its area will then be }A=\pi r^2\implies A=\pi \left( (1)/(\pi ) \right)^2\implies A=\cfrac{1}{\pi } \\\\ -------------------------------`


`\bf \textit{circumference of a circle}\\\\ C=2\pi r\quad \begin{cases} r=radius\\ -----\\ C=4 \end{cases}\implies 4=2\pi r\implies \cfrac{2}{\pi }=r \\\\\\ \textit{its area will then be }A=\pi r^2\implies A=\pi \left( (2)/(\pi ) \right)^2\implies A=\cfrac{4}{\pi }`

Answer 2

No. Area is proportional to the square of the linear dimension.

The area of the regular pancake is (4/2)^2 = 4 times that of the silver dollar pancake.