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polet [3.4K]
2 years ago
11

Trig: A sector of a circle has area 25 cm2 and centralangle

Mathematics
1 answer:
Alchen [17]2 years ago
3 0

Answer:  Radius = 10 cm and Arc length = 5 cm

Step-by-step explanation:

The area of a sector with radius r and central angle \theta (In radian) is given by :-

A=\dfrac{1}{2}r^2\theta

Given : A sector of a circle has area 25 cm^2 and central angle  0.5 radians.

Let r be the radius , then we have

25=\dfrac{1}{2}r^2(0.5)\\\\\Rightarrow\ r^2=\dfrac{2\times25}{0.5}\\\\\Rightarrow\ r^2=\dfrac{50}{0.5}=100\\\\\Rightarrow\ r=\sqrt{100}=10\ cm

Thus, radius = 10 cm

The length of arc is given by :-

l=r\theta=10\times0.5=5\ cm

Hence, the length of the arc = 5 cm

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