1955 AHSME Problems/Problem 15
Problem 15
The ratio of the areas of two concentric circles is . If the radius of the smaller is , then the difference between the radii is best approximated by:
Solution
Observe that there are 3 feet in 1 yard, 9 square feet in 1 square yard, and 27 cubic feet in 1 cubic yard.
This means that if the ratio is in 1D, it is in 2D, and it is in 3D.
We can apply this thinking into our current question, which would have in the 2D-plane. Since the radius is 1D, we would have to square root both sides to get
If we plug in for the smaller radius, we get The difference between the two sides would be (approximately)
See Also
1955 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.