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If the area of circle O is 16π, what is the length of an arc on the circle formed by a central angle measuring 45 degrees?
- a)π
- b)3π/2
- c)2π
- d)5π/2
- e)8π
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If the area of circle O is 16π, what is the length of an arc on the...
The area of a circle is given by the formula A = πr2, where A is the area and r is the radius of the circle.
In this case, the area of circle O is given as 16π. We can equate this to the formula to find the radius:
πr2 = 16π
Dividing both sides by π, we get:
r2 = 16
Taking the square root of both sides, we get:
r = 4
The length of an arc on a circle is given by the formula L = (θ/360) * 2πr, where L is the length of the arc, θ is the central angle in degrees, and r is the radius of the circle.
In this case, the central angle is given as 45 degrees and the radius is 4. Substituting these values into the formula, we get:
L = (45/360) * 2π(4)
L = (1/8) * 2π(4)
L = (1/8) * 8π
L = π
L = (1/8) * 2π(4)
L = (1/8) * 8π
L = π
Hence, the length of the arc is π. Therefore, the correct answer is option A.
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