Find the area of a quadrant of a circle whose circumference is 22cm.

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle.
Given that the circumference is 22cm, we have:
22 = 2πr
r = 22 / (2π) = 11/π cm
The area of a circle is given by the formula A = πr².
Substituting the value of r, we get:
A = π * (11/π)² = π * (121/π²) = 121/π cm²
A quadrant is one-fourth of a circle. Therefore, the area of a quadrant is:
Area of quadrant = (1/4) * A = (1/4) * (121/π) cm²
Using the approximation π ≈ 22/7, we have:
Area of quadrant = (1/4) * (121/(22/7)) = (1/4) * (121 * 7/22) = (1/4) * (637/22) = (1/4) * (77/2.62857) = (1/4) * 29.2893 ≈ 7.3223 cm²
Alternatively, using π ≈ 3.14:
Area of quadrant = (1/4) * (121/3.14) ≈ (1/4) * 38.52 ≈ 9.63 cm²
Therefore, the area of the quadrant is approximately 7.3223 cm² (using π ≈ 22/7) or 9.63 cm² (using π ≈ 3.14).