Question

A circle has a radius of 7 inches. Find the arc length intercepted by a central angle of 280°.​

Answer 1

Answer:

I think it will be Perimeter=2π(7)=14π=43.96

Arc length=280/360 (43.96)=39.56inches

Answer 2

The arc length intercepted by a central angle of 280° is 34.22 inches.

Given:

Radius of the circle = 7 inches.

Central angle at which arc intercepted = 280°

To Find:

The arc length.

Solution:

We know that;

Arc length is calculated by the formula:

S = rФ

Where,

S is the arc length

r is the radius of the circle.

Ф is the central angle in radians

Here,

r = 7 inches

Ф = 280°

We need to convert the central angle in radians unit.

So, for converting degrees into radians, we multiply the angle by $\pi /180$.

Hence, 280° = (280 x $\pi /180$) radians

=> 14π/9

Hence, the central angle is 14π/9.

Now, let us calculate the arc length.

Arc length(S) = 7 x 14π/9 inches

=> 34.22 inches

Hence, the arc length intercepted by a central angle of 280 degrees is 34.22 inches.

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