Class 5 Exam > Class 5 Questions > Which of the following is correct?a)Only a li...
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Which of the following is correct?
- a)Only a limited number of radii can be drawn in a circle.
- b)An infinite number of diameters can be drawn in a circle.
- c)Some of the diameters do not pass through the centre of the circle.
- d)A circle may have infinite number of centres.
Correct answer is option 'B'. Can you explain this answer?
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Which of the following is correct?a)Only a limited number of radii can...
We can draw infinite lines that pass through the center of the circle with endpoints on the circumference of the circle. Hence, a circle can have countless number of diameters.
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Which of the following is correct?a)Only a limited number of radii can...
Answer:
A circle is a closed shape consisting of all points in a plane that are equidistant from a fixed point called the center. Let's analyze each of the given options to determine which one is correct.
Option a) Only a limited number of radii can be drawn in a circle:
- A radius is a line segment that joins the center of a circle to any point on its circumference.
- In a circle, there are an infinite number of radii.
- Starting from the center, you can draw a radius to any point on the circumference.
- Therefore, option a) is incorrect.
Option b) An infinite number of diameters can be drawn in a circle:
- A diameter is a line segment that passes through the center of a circle and has both endpoints on the circumference.
- In a circle, there are an infinite number of diameters.
- Every radius can be extended to become a diameter by connecting two points on the circumference.
- Additionally, diameters can be drawn at any angle through the center of the circle.
- Therefore, option b) is correct.
Option c) Some of the diameters do not pass through the center of the circle:
- By definition, a diameter must pass through the center of a circle.
- It is not possible to have a diameter that does not pass through the center.
- Therefore, option c) is incorrect.
Option d) A circle may have an infinite number of centers:
- The center of a circle is a fixed point equidistant from all points on its circumference.
- A circle can only have one center.
- If there were multiple centers, the distances from the points on the circumference to each center would not be equal.
- Therefore, option d) is incorrect.
Conclusion:
The correct answer is option b) An infinite number of diameters can be drawn in a circle. This is because a diameter is a line segment that passes through the center of a circle and has both endpoints on the circumference. Every radius can be extended to become a diameter, and diameters can be drawn at any angle through the center.
A circle is a closed shape consisting of all points in a plane that are equidistant from a fixed point called the center. Let's analyze each of the given options to determine which one is correct.
Option a) Only a limited number of radii can be drawn in a circle:
- A radius is a line segment that joins the center of a circle to any point on its circumference.
- In a circle, there are an infinite number of radii.
- Starting from the center, you can draw a radius to any point on the circumference.
- Therefore, option a) is incorrect.
Option b) An infinite number of diameters can be drawn in a circle:
- A diameter is a line segment that passes through the center of a circle and has both endpoints on the circumference.
- In a circle, there are an infinite number of diameters.
- Every radius can be extended to become a diameter by connecting two points on the circumference.
- Additionally, diameters can be drawn at any angle through the center of the circle.
- Therefore, option b) is correct.
Option c) Some of the diameters do not pass through the center of the circle:
- By definition, a diameter must pass through the center of a circle.
- It is not possible to have a diameter that does not pass through the center.
- Therefore, option c) is incorrect.
Option d) A circle may have an infinite number of centers:
- The center of a circle is a fixed point equidistant from all points on its circumference.
- A circle can only have one center.
- If there were multiple centers, the distances from the points on the circumference to each center would not be equal.
- Therefore, option d) is incorrect.
Conclusion:
The correct answer is option b) An infinite number of diameters can be drawn in a circle. This is because a diameter is a line segment that passes through the center of a circle and has both endpoints on the circumference. Every radius can be extended to become a diameter, and diameters can be drawn at any angle through the center.
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Which of the following is correct?a)Only a limited number of radii can be drawn in a circle.b)An infinite number of diameters can be drawn in a circle.c)Some of the diameters do not pass through the centre of the circle.d)A circle may have infinite number of centres.Correct answer is option 'B'. Can you explain this answer?
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