Question

If the area of a sector of a circle is 5/18 th of the area of that circle,

then find the central angle of the sector​

Answer 1

Answer:

If the Area of a Sector of a Circle is 5 18 of the Area of the Circle, Then the Sector Angle is Equal to Concept: Areas Related to Circles Examples and Solutions.

Answer 2

Given:

If the area of a sector of a circle is 5/18th of the area of the circle

To Find:

Find the central angle of the sector

Solution:

A circle is a 2-dimensional figure in which the distance of all the points on the perimeter is the same as the centre of the circle.

A sector is a part of the circle with some angle subtending at the centre which should be less than 360 degrees

The formula for the area of a sector is,

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

The area of the circle can be measured by,

$A=\pi r^2$

Now it is given that area of a sector of a circle is 5/18th of the area of the circle, now put the values taking it as the ratio of the area of the sector to the area of the circle,

$\frac{5}{18} =\frac{\pi r^2\frac{\theta}{360} }{\pi r^2} \\\frac{5}{18} =\frac{\theta}{360} \\\theta=100$

Hence, the central angle of the sector is 100 degrees.