Difference between revisions of "1952 AHSME Problems/Problem 1"
Yjc64002776 (talk | contribs) (→Solution 2) |
Yjc64002776 (talk | contribs) (→Solution 2) |
||
| (One intermediate revision by the same user not shown) | |||
| Line 12: | Line 12: | ||
==Solution 2== | ==Solution 2== | ||
| − | The phrasing of the problem makes it clear that the rule would apply to all rational radii. So let r be equal to one. <math>\pi</math> times | + | The phrasing of the problem makes it clear that the rule would apply to all rational radii. So let r be equal to one. <math>\pi</math> times 1 squared is equal to <math>\pi</math> which is irrational. Therefore, the answer is <math>\boxed{B}.</math> |
~YJC64002776 | ~YJC64002776 | ||
Latest revision as of 10:34, 19 January 2021
Contents
Problem
If the radius of a circle is a rational number, its area is given by a number which is:
Solution
Let the radius of the circle be the common fraction 
Then the area of the circle is 
Because 
is irrational and 
is rational, their product must be irrational. The answer is 
Solution 2
The phrasing of the problem makes it clear that the rule would apply to all rational radii. So let r be equal to one. times 1 squared is equal to which is irrational. Therefore, the answer is
~YJC64002776
See also
| 1952 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by First Question |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
