Difference between revisions of "2020 AMC 10A Problems/Problem 16"
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== Solution == | == Solution == | ||
+ | We consider an individual one by one block. | ||
+ | If we draw a quarter of a circle from each corner, the area covered by the circles should be <math>0.5</math>. Because of this, and the fact that there are four circles, we write | ||
+ | |||
+ | <cmath>4 * \frac{1}{4} * \pi r^2 = \frac{1}{2}</cmath>. | ||
+ | |||
+ | Solving for <math>r</math>, we obtain <math>r = \frac{1}{\sqrt{2\pi}}</math>, where with <math>\pi \approx 3</math>, we get <math>r = \frac{1}{\sqrt{6}}</math>, and from here, we simplify and see that <math>r \approx 0.4 \implies {\textbf{(B) } 0.4.}</math> | ||
==See Also== | ==See Also== |
Revision as of 22:52, 31 January 2020
Problem
A point is chosen at random within the square in the coordinate plane whose vertices are and
. The probability that the point is within
units of a lattice point is
. (A point
is a lattice point if
and
are both integers.) What is
to the nearest tenth
Solution
We consider an individual one by one block.
If we draw a quarter of a circle from each corner, the area covered by the circles should be . Because of this, and the fact that there are four circles, we write
.
Solving for , we obtain
, where with
, we get
, and from here, we simplify and see that
See Also
2020 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 15 |
Followed by Problem 17 | |
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 | ||
All AMC 10 Problems and Solutions |
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