1962 AHSME Problems/Problem 5
Problem
If the radius of a circle is increased by unit, the ratio of the new circumference to the new diameter is:
Solution (Intuitive)
The ratio of a circumference to a diameter always is the same so the answer is obviously C.
Solution 2 (Full Proof)
Let us say that the radius of a circle is . When the radius is increased by , the new radius is so the diameter is . We know that the circumference of a circle is so . Finally, the problem asked for the ratio of the new circumference to the new diameter is .
~Mathfun1000
See Also
1962 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
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