Problem: If four times the reciprocal of the circumference of a circle equals the diameter of the circle, then the area of the circle is
Answer Choices:
A. 1Ο2\dfrac{1}{\pi^{2}}Ο21β
B. 1Ο\dfrac{1}{\pi}Ο1β
C. 111
D. Ο\piΟ
E. Ο2\pi^{2}Ο2 Solution:
If rrr and AAA are the radius and area of the circle, respectively, then
42Οr=2r4=4Οr21=Οr2=A.\begin{aligned} \dfrac{4}{2 \pi r} & =2 r \\ 4 & =4 \pi r^{2} \\ 1 & =\pi r^{2}=A . \end{aligned} 2Οr4β41β=2r=4Οr2=Οr2=A.β