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zaharov [31]
3 years ago
12

Use the fact that the length of an arc intercepted by an angle is proportional to the radius to find the arc length given the ci

rcle area A = 16π cm2 and Θ = π 3 .
Mathematics
2 answers:
nadezda [96]3 years ago
7 0
Answer: The length of the arc is: L=4π/3 cm

Length of arc: L=?
<span>
L=r Θ
</span>
Central angle: Θ=<span>π/3
Radius: r=?

Area of the circle: A=</span><span>16π cm^2

A=</span>π r^2

Replacing A=16π cm2 in the equation above:
16π cm^2=π r^2

Solving for r: Dividing both sides of the formula by π:
(16π cm^2)/π=(π r^2)/π

16 cm^2=r^2

Square root both sides of the formula:
sqrt( 16 cm^2)=sqrt(r^2)
4 cm=r
r=4 cm

L=r Θ
L=(4 cm)π/3
L=4π/3 cm
REY [17]3 years ago
4 0

Answer:

4π/3 cm

Step-by-step explanation:

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