1950 AHSME Problems/Problem 8: Difference between revisions
Created page with "== Problem== If the radius of a circle is increased <math>100\%</math>, the area is increased: <math> \textbf{(A)}\ 100\%\qquad\textbf{(B)}\ 200\%\qquad\textbf{(C)}\ 300\%\qqua..." |
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==Solution== | ==Solution== | ||
Increasing by < | Increasing by <imath>100\%</imath> is the same as doubling the radius. If we let <imath>r</imath> be the radius of the old circle, then the radius of the new circle is <imath>2r.</imath> | ||
Since the area of the circle is given by the formula < | Since the area of the circle is given by the formula <imath>\pi r^2,</imath> the area of the new circle is <imath>\pi (2r)^2 = 4\pi r^2.</imath> The area is quadrupled, or increased by <imath>\boxed{\mathrm{(C) }300\%.}</imath> | ||
==See Also== | ==See Also== | ||
{{AHSME box|year=1950|num-b=7|num-a=9}} | {{AHSME 50p box|year=1950|num-b=7|num-a=9}} | ||
[[Category:Introductory Algebra Problems]] | |||
{{MAA Notice}} | |||
Latest revision as of 17:45, 9 November 2025
Problem
If the radius of a circle is increased 
, the area is increased:
Solution
Increasing by is the same as doubling the radius. If we let 
be the radius of the old circle, then the radius of the new circle is 
Since the area of the circle is given by the formula 
the area of the new circle is 
The area is quadrupled, or increased by 
See Also
| 1950 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
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