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A race track is in the form of a ring whose inner and outer circumference are 437 m and 50 m respectively. Find the area of the track.
- a)4935 m2
- b)4065 m2
- c)4135 m2
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A race track is in the form of a ring whose inner and outer circumfere...
To find the area of the track, we need to subtract the area of the inner circle from the area of the outer circle.
First, let's find the radius of the inner and outer circles using the given circumferences.
- The inner circumference is given as 437 m. We can use the formula for the circumference of a circle, C = 2πr, where C is the circumference and r is the radius. Plugging in the given value, we have:
437 = 2πr
Dividing both sides by 2π, we get:
r = 437 / (2π)
r ≈ 69.5 m
- The outer circumference is given as 50 m. Using the same formula, we have:
50 = 2πR
Dividing both sides by 2π, we get:
R = 50 / (2π)
R ≈ 7.96 m
Now that we have the radius of the inner circle (r) and the outer circle (R), we can find their areas.
- The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.
- The area of the inner circle is:
A_inner = πr^2
A_inner = π(69.5)^2
A_inner ≈ 15141.32 m^2
- The area of the outer circle is:
A_outer = πR^2
A_outer = π(7.96)^2
A_outer ≈ 199.16 m^2
Now, subtract the area of the inner circle from the area of the outer circle to find the area of the track:
Area of the track = A_outer - A_inner
Area of the track ≈ 199.16 m^2 - 15141.32 m^2
Area of the track ≈ -14942.16 m^2
Since the calculated area is negative, it means there might be an error in the given measurements or calculations. None of the provided answer options are correct.
First, let's find the radius of the inner and outer circles using the given circumferences.
- The inner circumference is given as 437 m. We can use the formula for the circumference of a circle, C = 2πr, where C is the circumference and r is the radius. Plugging in the given value, we have:
437 = 2πr
Dividing both sides by 2π, we get:
r = 437 / (2π)
r ≈ 69.5 m
- The outer circumference is given as 50 m. Using the same formula, we have:
50 = 2πR
Dividing both sides by 2π, we get:
R = 50 / (2π)
R ≈ 7.96 m
Now that we have the radius of the inner circle (r) and the outer circle (R), we can find their areas.
- The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.
- The area of the inner circle is:
A_inner = πr^2
A_inner = π(69.5)^2
A_inner ≈ 15141.32 m^2
- The area of the outer circle is:
A_outer = πR^2
A_outer = π(7.96)^2
A_outer ≈ 199.16 m^2
Now, subtract the area of the inner circle from the area of the outer circle to find the area of the track:
Area of the track = A_outer - A_inner
Area of the track ≈ 199.16 m^2 - 15141.32 m^2
Area of the track ≈ -14942.16 m^2
Since the calculated area is negative, it means there might be an error in the given measurements or calculations. None of the provided answer options are correct.
Community Answer
A race track is in the form of a ring whose inner and outer circumfere...
Let R be the radius of outer circle and r be the radius of inner circle.
2πR = 503
and 2πr = 437
Width of the track = R - r =
2πR = 503
and 2πr = 437
Width of the track = R - r =
Area of the track = π(R2 - r2)
= π(R+ r) (R - r)
= 4935 m2
= π(R+ r) (R - r)
= 4935 m2
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A race track is in the form of a ring whose inner and outer circumference are 437 m and 50 m respectively. Find the area of the track.a)4935 m2b)4065 m2c)4135 m2d)None of theseCorrect answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A race track is in the form of a ring whose inner and outer circumference are 437 m and 50 m respectively. Find the area of the track.a)4935 m2b)4065 m2c)4135 m2d)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A race track is in the form of a ring whose inner and outer circumference are 437 m and 50 m respectively. Find the area of the track.a)4935 m2b)4065 m2c)4135 m2d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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