1950 AHSME Problems/Problem 34
Problem
When the circumference of a toy balloon is increased from inches to inches, the radius is increased by:
Solutions
Solution 1
When the circumference of a circle is increased by a percentage, the radius is also increased by the same percentage (or else the ratio of the circumference to the diameter wouldn't be anymore) We see that the circumference was increased by . This means the radius was also increased by . The radius of the original balloon is . With the increase, it becomes . The increase is .
Solution 2
The radii of the circles are and , respectively. The positive difference is therefore .
Solution 3
Let the radius of the circle with the larger circumference be and the circle with the smaller circumference be . Calculating the ratio of the two
See Also
1950 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 33 |
Followed by Problem 35 | |
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