Question

The area of a sector of a circle with a central angle of 150° is 73 m^2. Find the radius of the circle.

Answer 1

The radius of the circle with sector area 73 square meters and centeral angle 150 degrees is 7.5m.

According to the given question.

The area of the sector of the circle is 73 square meter.

And, central angle, θ = 150 degrees

Since, if θ is the angle substended at center of the circle with radius r, then the area of sector of a circle is given by

$A = \frac{\theta}{360^{o} } \times \pi r^{2}$

Where,

A is the area of sector

And, π = 3.14

Thereore, the radius of the circle with the sector area 73 square meter and central angle 150 degrees is given by

$73 = \frac{150}{360} \times 3.14\times (radius)^{2}$

$\implies 73 = 0.4166\times 3.14\times(radius)^{2}$

$\implies (radius)^{2} = \frac{73}{0.4166\times\ 3.14}$

$\implies (radius)^{2} = \frac{73}{1.30}$

$\implies (radius)^{2} = 56.153$

⇒ radius = √56.153

⇒ radius = 7.49 ≈ 7.5m

Hence, the radius of the circle with sector area 73 square meters and centeral angle 150 degrees is 7.5m.

Find out more information about sector area and radius of the circle here:

brainly.com/question/15849991

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