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The length of arc XY of a circle is equal to 1/6 of the circumference of the circle. The length of the arc is 7n inches. What is the radius, in inches, of the circle?
- a)42
- b)21
- c)14
- d)7
- e)3
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The length of arc XY of a circle is equal to 1/6 of the circumference ...
Given information:
- The length of arc XY is equal to 1/6 of the circumference of the circle.
- The length of the arc is 7n inches.
To find: The radius of the circle.
Let's solve this step by step:
1. Finding the circumference of the circle:
- The length of arc XY is equal to 1/6 of the circumference.
- So, 1/6 of the circumference = 7n inches.
- Multiplying both sides by 6, we get: circumference = 42n inches.
2. Finding the radius of the circle:
- The circumference of a circle is given by the formula: circumference = 2πr, where r is the radius.
- Substituting the value of circumference (42n inches) into the formula, we get: 42n = 2πr.
- Dividing both sides by 2π, we get: r = (42n) / (2π).
- Simplifying the expression, we have: r = 21n / π.
Therefore, the radius of the circle is 21n / π inches.
Explanation:
The answer is option 'B' because the radius of the circle is given by the expression 21n / π. The value of n is not given in the question, so we cannot determine the exact value of the radius. However, we can conclude that the radius is directly proportional to n. As n increases, the radius will also increase. Since the radius is given in terms of n, the answer cannot be a specific number or an exact value. The correct answer is therefore option 'B', as it represents the general form of the radius in terms of n.
- The length of arc XY is equal to 1/6 of the circumference of the circle.
- The length of the arc is 7n inches.
To find: The radius of the circle.
Let's solve this step by step:
1. Finding the circumference of the circle:
- The length of arc XY is equal to 1/6 of the circumference.
- So, 1/6 of the circumference = 7n inches.
- Multiplying both sides by 6, we get: circumference = 42n inches.
2. Finding the radius of the circle:
- The circumference of a circle is given by the formula: circumference = 2πr, where r is the radius.
- Substituting the value of circumference (42n inches) into the formula, we get: 42n = 2πr.
- Dividing both sides by 2π, we get: r = (42n) / (2π).
- Simplifying the expression, we have: r = 21n / π.
Therefore, the radius of the circle is 21n / π inches.
Explanation:
The answer is option 'B' because the radius of the circle is given by the expression 21n / π. The value of n is not given in the question, so we cannot determine the exact value of the radius. However, we can conclude that the radius is directly proportional to n. As n increases, the radius will also increase. Since the radius is given in terms of n, the answer cannot be a specific number or an exact value. The correct answer is therefore option 'B', as it represents the general form of the radius in terms of n.
Community Answer
The length of arc XY of a circle is equal to 1/6 of the circumference ...
To solve this problem, you must remember that the formula for the circumference of a circle is C = 2πr, where r is the radius.
You are given that the length of arc XY is 7π, and that this is 1/6 of the total circumference. Therefore, the circumference must be 6 × 7π = 42π. Substitute this value for C in the equation and solve for r, as follows:
42π = 2πr
21π = πr
21 = r
You are given that the length of arc XY is 7π, and that this is 1/6 of the total circumference. Therefore, the circumference must be 6 × 7π = 42π. Substitute this value for C in the equation and solve for r, as follows:
42π = 2πr
21π = πr
21 = r
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The length of arc XY of a circle is equal to 1/6 of the circumference of the circle. The length of the arc is 7n inches. What is the radius, in inches, of the circle?a)42b)21c)14d)7e)3Correct answer is option 'B'. Can you explain this answer?
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The length of arc XY of a circle is equal to 1/6 of the circumference of the circle. The length of the arc is 7n inches. What is the radius, in inches, of the circle?a)42b)21c)14d)7e)3Correct answer is option 'B'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about The length of arc XY of a circle is equal to 1/6 of the circumference of the circle. The length of the arc is 7n inches. What is the radius, in inches, of the circle?a)42b)21c)14d)7e)3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of arc XY of a circle is equal to 1/6 of the circumference of the circle. The length of the arc is 7n inches. What is the radius, in inches, of the circle?a)42b)21c)14d)7e)3Correct answer is option 'B'. Can you explain this answer?.
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