The area of a circle is 90. Find the area of a sector of this circle, the central angle of which is 60

From the condition, we know that the area of the circle is 90, and we also know that the central angle is 60 °.

In order to find the area of a sector of a circle, let’s compose and solve the proportion.

The circle is 360 °. Let’s write down:

360 ° – 90;

Let’s denote the area of a sector with a central angle of 120 ° using the variable x.

60 ° – x.

Let’s make the proportion:

360/60 = 90 / x;

We have to find the unknown extreme term of the proportion, for this we divide the product of the middle terms by the known extreme term of the proportion:

x = (60 * 90) / 360 = 5400/360 = 15 sq. units.