Key to "An arc is 6.5 cm long and it..."

Braxton Pugh

Answered question

2021-08-06

An arc is 6.5 cm long and it subtends a central angle of 45°. Find the radius of the circle.

pivonie8

Skilled2021-08-07Added 91 answers

Use the arc length formula:

$L = 2 π r \cdot (θ / 360 °)$

where r is the radius and $θ$ is the central angle.

Subtitute $L = 6.5$ cm and $θ = 45^{\circ}$ then solve for r:

$6.5 = (π / 4) r$

Multiply both sides by $4 / π$ :

$6.5 \cdot (4 / π) = r$

$r \sim 8.3 c m$

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