Krishna
0

Step 1: Note down the given values

Step 2: Set up the formula for arc length.

NOTE: The formula is arc length (s) = \frac{\theta}{360} *C

Where, s = Arc length

C = Circumference

\theta = Central Angle

Step 3: Calculate the circumference of the circle by using the area.

Skill 1: Write the formulas of the area and circumference of the circle.

NOTE: Area = \pi r^2

Circumference = 2 \pi r

Skill 2: Calculate the radius of the circle by using the area formula

Area = \pi r^2

46 = \pi r^2

r^2 = \frac{46}{\pi}

r = \sqrt{\frac{46}{\pi}}

Skill 3: Substitute the radius(r) value in the circumference formula.

Circumference = 2 \pi r

C =   2 \pi \sqrt{\frac{46}{\pi}}

Step 4: Plug the value of  circumference (C) into the formula

Step 5: Plug the value of the arc’s central angle into the formula.

Step 6: Simplify the equation to find the arc length

NOTE: Use multiplication and division to simplify the equation.

EXAMPLE: arc length (s) = \frac{26}{360}*2\pi\sqrt{\frac{46}{\pi}}

Arc\ lengths\ \left(s\right)=1.736