Question

Find the length of the arc, s, on a circle of radius r intercepted by a central angle θ. Express the arc length in terms of π. Then round your answer to two decimal places.

Radius, r=7 inches; Central angle, θ = 35⁰

Answer 1

The arc length, s, of a circle with a radius of 7 inches and a central angle of 35 degrees is approximately 4.28 inches when rounded to two decimal places.

Step-by-step explanation:

To find the arc length, s, of a circle with a given radius, r, and a central angle θ in degrees, we use the formula:

s = r θ π / 180

In this case, with a radius r = 7 inches and a central angle θ = 35°, the calculation is:

s = 7 inches * 35° * π / 180°

We can simplify this by multiplying the numbers together and then dividing by 180:

s = (7 * 35 * π) / 180 = (245 * π) / 180

Now we calculate the numerical value:

s = 1.3611 * π (approximating π as 3.14159)

So the arc length s approximately equals:

s ≈ 1.3611 * 3.14159 ≈ 4.28 inches

Therefore, the arc length s is approximately 4.28 inches when rounded to two decimal places.