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°.