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04 Jun 2020, 04:21
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
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Question Stats:
48% (01:47) correct
52%
(01:54)
wrong
based on 175
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What is the maximum number of points that can be placed on a circular disk of radius 1 meter (some of the points could be placed on the bounding circle of the disk) such that no two points are at a distance of less than 1 meter from each other.
A)9
B)8
C)6
D)5
E)7
A)9
B)8
C)6
D)5
E)7
04 Jun 2020, 06:16
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To fit in as many points as possible, we'll want them to be as close together as possible, so (if we can) we want to make the distance between points 1 meter. Along a diameter, we can place three points -- one at the center, and two on the circumference. If we have a point at the center, every other point will need to be on the circumference, to be 1 meter away from the center.
So now we want points around the circumference that are 1 meter apart, in a straight line. If you take two consecutive points around the circumference, if they're 1 meter apart, and the radius is 1 meter, you'd make an equilateral triangle by connecting the two circumference points and the center. So there will be a 60 degree angle at the center, and going around the circle, you'll be able to place 6 points around the circumference that are 1 meter apart in a straight line (since 6*60 = 360). Including the center, we have 7 points in total.
So now we want points around the circumference that are 1 meter apart, in a straight line. If you take two consecutive points around the circumference, if they're 1 meter apart, and the radius is 1 meter, you'd make an equilateral triangle by connecting the two circumference points and the center. So there will be a 60 degree angle at the center, and going around the circle, you'll be able to place 6 points around the circumference that are 1 meter apart in a straight line (since 6*60 = 360). Including the center, we have 7 points in total.
04 Jun 2020, 08:36
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Circumference of the circle =2×3.14×1
= 6.28
So 6 points on the circle and one at center total 7
Option E is the answer
Posted from my mobile device
= 6.28
So 6 points on the circle and one at center total 7
Option E is the answer
Posted from my mobile device
