$20 \cdot 30$ If the radius of a circle is increased by $100 \%$, then the area increases by
(A) $100 \%$.
(B) $200 \%$.
(C) $300 \%$.
(C) $400 \%$.
(E) None of the above answers is correct.
(1st American High School Mathematics Examination, 1950)
[Solution] Let the radius of the circle be $r$, after increasing by $100\%$ it becomes $2r$. The new circle area increases by $4 \pi r^{2}-\pi r^{2}=3 \pi r^{2}$, the percentage increase in area is $\frac{3 \pi r^{2}}{\pi r^{2}} \cdot 100 \% = 300 \%$. Therefore, the answer is $(C)$.