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John Nash, an avid mathematician, had his room constructed such that the floor of the room was an equilateral triangle in shape instead of the usual rectangular shape. One day he brought home a bird and tied it to one end of a string and then tied the other end of the string to one of the corners of his room. The next day, he untied the other end of the string from the corner of the room and tied it to a point exactly at the center of the floor of the room. Assuming that the dimensions of the room are relatively large compared to the length of the string, find the number of times, by which the maximum possible space in which the bird can fly, increase.
- a)4
- b)5
- c)6
- d)7
Correct answer is option 'B'. Can you explain this answer?
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John Nash, an avid mathematician, had his room constructed such that t...
Consider the length of the string less than or equal to the inradius of the floor. At the comer of the floor you will find a sixth part of a hemisphere and at the centre it will be a hemisphere.
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John Nash, an avid mathematician, had his room constructed such that t...
Explanation:
To find the number of times the maximum possible space in which the bird can fly increases, we need to compare the areas of the two spaces - the space when the string is tied to the corner of the room and the space when the string is tied to the center of the room.
Step 1:
Let's consider the equilateral triangle as ABC, with AB, BC, and AC as the sides of the triangle. Let's assume the side length of the triangle to be 's'.
Step 2:
When the string is tied to one corner (let's say A) of the room, the bird can fly in the shape of a sector of a circle with radius 's' and angle 60 degrees (as it is an equilateral triangle). The area of this sector can be calculated using the formula:
Area of sector = (1/6) * π * s^2
Step 3:
When the string is tied to the center of the room, the bird can fly in the shape of a circle with radius 's' (as it is equidistant from all the corners of the triangle). The area of this circle can be calculated using the formula:
Area of circle = π * s^2
Step 4:
To find the increase in the maximum possible space, we need to calculate the ratio of the two areas:
Increase in space = (Area of circle) / (Area of sector)
= (π * s^2) / ((1/6) * π * s^2)
= 6
Step 5:
Therefore, the maximum possible space in which the bird can fly increases by a factor of 6.
Conclusion:
The correct answer is option B) 6.
To find the number of times the maximum possible space in which the bird can fly increases, we need to compare the areas of the two spaces - the space when the string is tied to the corner of the room and the space when the string is tied to the center of the room.
Step 1:
Let's consider the equilateral triangle as ABC, with AB, BC, and AC as the sides of the triangle. Let's assume the side length of the triangle to be 's'.
Step 2:
When the string is tied to one corner (let's say A) of the room, the bird can fly in the shape of a sector of a circle with radius 's' and angle 60 degrees (as it is an equilateral triangle). The area of this sector can be calculated using the formula:
Area of sector = (1/6) * π * s^2
Step 3:
When the string is tied to the center of the room, the bird can fly in the shape of a circle with radius 's' (as it is equidistant from all the corners of the triangle). The area of this circle can be calculated using the formula:
Area of circle = π * s^2
Step 4:
To find the increase in the maximum possible space, we need to calculate the ratio of the two areas:
Increase in space = (Area of circle) / (Area of sector)
= (π * s^2) / ((1/6) * π * s^2)
= 6
Step 5:
Therefore, the maximum possible space in which the bird can fly increases by a factor of 6.
Conclusion:
The correct answer is option B) 6.
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John Nash, an avid mathematician, had his room constructed such that the floor of the room was an equilateral triangle in shape instead of the usual rectangular shape. One day he brought home a bird and tied it to one end of a string and then tied the other end of the string to one of the corners of his room. The next day, he untied the other end of the string from the corner of the room and tied it to a point exactly at the center of the floor of the room. Assuming that the dimensions of the room are relatively large compared to the length of the string, find the number of times, by which the maximum possible space in which the bird can fly, increase.a)4b)5c)6d)7Correct answer is option 'B'. Can you explain this answer?
Question Description
John Nash, an avid mathematician, had his room constructed such that the floor of the room was an equilateral triangle in shape instead of the usual rectangular shape. One day he brought home a bird and tied it to one end of a string and then tied the other end of the string to one of the corners of his room. The next day, he untied the other end of the string from the corner of the room and tied it to a point exactly at the center of the floor of the room. Assuming that the dimensions of the room are relatively large compared to the length of the string, find the number of times, by which the maximum possible space in which the bird can fly, increase.a)4b)5c)6d)7Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about John Nash, an avid mathematician, had his room constructed such that the floor of the room was an equilateral triangle in shape instead of the usual rectangular shape. One day he brought home a bird and tied it to one end of a string and then tied the other end of the string to one of the corners of his room. The next day, he untied the other end of the string from the corner of the room and tied it to a point exactly at the center of the floor of the room. Assuming that the dimensions of the room are relatively large compared to the length of the string, find the number of times, by which the maximum possible space in which the bird can fly, increase.a)4b)5c)6d)7Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for John Nash, an avid mathematician, had his room constructed such that the floor of the room was an equilateral triangle in shape instead of the usual rectangular shape. One day he brought home a bird and tied it to one end of a string and then tied the other end of the string to one of the corners of his room. The next day, he untied the other end of the string from the corner of the room and tied it to a point exactly at the center of the floor of the room. Assuming that the dimensions of the room are relatively large compared to the length of the string, find the number of times, by which the maximum possible space in which the bird can fly, increase.a)4b)5c)6d)7Correct answer is option 'B'. Can you explain this answer?.
John Nash, an avid mathematician, had his room constructed such that the floor of the room was an equilateral triangle in shape instead of the usual rectangular shape. One day he brought home a bird and tied it to one end of a string and then tied the other end of the string to one of the corners of his room. The next day, he untied the other end of the string from the corner of the room and tied it to a point exactly at the center of the floor of the room. Assuming that the dimensions of the room are relatively large compared to the length of the string, find the number of times, by which the maximum possible space in which the bird can fly, increase.a)4b)5c)6d)7Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about John Nash, an avid mathematician, had his room constructed such that the floor of the room was an equilateral triangle in shape instead of the usual rectangular shape. One day he brought home a bird and tied it to one end of a string and then tied the other end of the string to one of the corners of his room. The next day, he untied the other end of the string from the corner of the room and tied it to a point exactly at the center of the floor of the room. Assuming that the dimensions of the room are relatively large compared to the length of the string, find the number of times, by which the maximum possible space in which the bird can fly, increase.a)4b)5c)6d)7Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for John Nash, an avid mathematician, had his room constructed such that the floor of the room was an equilateral triangle in shape instead of the usual rectangular shape. One day he brought home a bird and tied it to one end of a string and then tied the other end of the string to one of the corners of his room. The next day, he untied the other end of the string from the corner of the room and tied it to a point exactly at the center of the floor of the room. Assuming that the dimensions of the room are relatively large compared to the length of the string, find the number of times, by which the maximum possible space in which the bird can fly, increase.a)4b)5c)6d)7Correct answer is option 'B'. Can you explain this answer?.
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