Check the solution to "Two circles are concentric. The smaller circle has..."

High School
Geometry
High school geometry
Circles

Mark Johns

Answered question

2022-03-03

Two circles are concentric. The smaller circle has a radius of 8 cm and the larger circle has a radius of 12 cm. A central angle forms an arc on both circles. If the length of the arc on the smaller circle is 17 cm, then what is the length of the arc on the larger circle?
a) 25.5 cm
b) 11.3 cm
c) 17.7 cm
d) 5.6 cm

Answer & Explanation

Capodarcod0f

Beginner2022-03-04Added 6 answers

Step 1
Let

r = 8 c m, R = 12 c m

θ

he central angle.
Let S he are of small circle and v he are of large wile

S = \frac{θ}{360^{\circ}} \times 2 π r

17 = \frac{θ}{360^{\circ}} \times 2 π (8)

θ = \frac{17 \times 360}{16 π} = \frac{765}{2 π}

θ = \frac{765}{2 π}

Step 2

V = \frac{θ}{360} \times 2 π R

= \frac{765}{2 π \times 360} \times 2 π \times 12

= 25.5

cm
Therefore, length of are large wile is 25.5 cm

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