The radius of the circle is 6 cm. Find the area of the sector, measured at an angle of 90 °.

Using the formula for the area of a circle S = πr ^ 2, where S is the area of the circle, r is the radius of the circle, π is the number pi, we find the area of this circle.

According to the condition of the problem, the radius of the circle is 6 cm, therefore, the area S of this circle is:

S = π6 ^ 2 = 36π cm ^ 2.

Let us find what part of the area of the circle is a sector with an angle equal to 90 °.

Since 360/90 = 4, then the area of the sector with an angle equal to 90 ° is 1/4 of the area of the circle and in this case it turns out to be:

36π / 4 = 9π cm ^ 2.

Answer: a sector with an angle equal to 90 ° is 9π cm ^ 2.