The area of the sector of a circle of radius 12 cm is 65 cm square the central angle of the sector is

the area of the sector of a circle of radius 12 cm is 65 cm square the central angle of the sector is

The area of the sector of a circle

Answer:

To find the central angle of the sector when the area of the sector and the radius are given, we can use the formula for the area of a sector of a circle. The formula for the area of a sector is \frac{A}{\pi r^2} , where A is the area of the sector, r is the radius of the circle, and \pi is a constant approximately equal to 3.14.

Given that the area of the sector is 65 cm² and the radius is 12 cm, we can plug these values into the formula:

65 = \frac{x}{\pi \times 12^2}

65 = \frac{x}{144\pi}

x = 65 \times 144\pi

x = 9360\pi

So, the area of the sector is 9360\pi cm².

To find the central angle of the sector, we use the formula \theta = \frac{A}{\pi r^2} \times 360° , where \theta is the central angle in degrees.

Plugging in the values we found earlier:

\theta = \frac{9360\pi}{\pi \times 12^2} \times 360°

\theta = 65 \times 30

\theta = 1950°

Therefore, the central angle of the sector is 1950°.