Work Shown:
L = arc length
L = (radius)*(central angle in radians)
L = (4.5 cm)*(pi/2 radians)
L = (4.5*pi/2) cm
L = (4.5*3.14/2) cm
L = 7.065 cm
L = 7.1 cm
Side note: the central angle must be in radians for that formula to work.
Answer:
(d) 7.1 cm
Step-by-step explanation:
The arc length is given by ...
s = rθ . . . . where r is the radius and θ is the arc length in radians
Put your given values in the formula and do the arithmetic.
s = (4.5 cm)(3.14/2) = 7.065 cm ≈ 7.1 cm
_____
Additional comment
Among the given answer choices, you can choose the correct one based on your knowledge of angle values and the sides of a right triangle. Here the angle is π/2 radians = 90°, so you're concerned with the length of a quarter circle. It will be longer than the radius, but shorter than 2 times the radius (a square corner). The only answer choice greater than the radius length is the correct one.
