A circle has a radius of 4 inches. In inches, what is the length of the arc intercepted by a central angle of 2 radians?
which of the following is the answer:
1) 2 radian
2) 2
3) 8 radian
4) 8
the answer is choice 4 idiot
To find the length of the arc intercepted by a central angle, you can use the formula:
Arc Length = (Central angle / 2π) * 2πr
Where:
- Central angle is given as 2 radians.
- π (pi) is approximately equal to 3.14159.
- r is the radius, given as 4 inches.
Now, substitute the given values into the formula:
Arc Length = (2 / 2π) * 2π * 4
Simplifying:
Arc Length = 2 * 4
Arc Length = 8 inches
Therefore, the correct answer is option 4) 8.
To find the length of an arc intercepted by a central angle, you can use the formula:
Arc Length = (Central Angle / 2π) × (2π × radius)
In this case, the radius of the circle is given as 4 inches and the central angle is given as 2 radians.
Plugging these values into the formula, we get:
Arc Length = (2 / 2π) × (2π × 4)
Simplifying the expression, we have:
Arc Length = 1 × 8π
Since the question asks for the length of the arc in inches, we need to convert the answer from radians to inches. Remember that 1 radian is equivalent to the radius length, so the arc length in inches is 8 × 4 = 32 inches.
Therefore, the correct answer is 32 inches, which is not listed among the options you provided.