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

Use the arc length formula: L=2πr×(θ360∘) where r is the radius and θ is the central angle Subtitute L=6.5cm and θ=45∘ then solve for r: 6.5=2πr×(45∘360∘) 6.5=(π4)r Multiply both sides by 4π: 6.5×(4π)=r r∼8.3cm

"An arc is 6.5 cm long and it..." was answered by our experts

High School
Geometry
High school geometry
Circles

ka1leE

Answered question

2021-06-19

An arc is 6.5 cm long and it subtends a central angle of $45^{\circ}$ . Find the radius of the circle.

Answer & Explanation

AGRFTr

Skilled2021-06-20Added 95 answers

Use the arc length formula: $L = 2 π r \times (\frac{θ}{360^{\circ}})$

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

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

$6.5 = 2 π r \times (\frac{45^{\circ}}{360^{\circ}})$

$6.5 = (\frac{π}{4}) r$

Multiply both sides by $\frac{4}{π} :$

$6.5 \times (\frac{4}{π}) = r$

$r \sim 8.3 c m$

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