1950 AHSME Problems/Problem 8

Problem

If the radius of a circle is increased $100\%$ , the area is increased:

$\textbf{(A)}\ 100\%\qquad\textbf{(B)}\ 200\%\qquad\textbf{(C)}\ 300\%\qquad\textbf{(D)}\ 400\%\qquad\textbf{(E)}\ \text{By none of these}$

Solution

Increasing by $100\%$ is the same as doubling the radius. If we let $r$ be the radius of the old circle, then the radius of the new circle is $2r.$

Since the area of the circle is given by the formula $\pi r^2,$ the area of the new circle is $\pi (2r)^2 = 4\pi r^2.$ The area is quadrupled, or increased by $\boxed{\mathrm{(C) }300\%.}$

1950 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 7	Followed by Problem 9
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1950 AHSME Problems/Problem 8

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