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

To find the area of a quadrant of a circle, we first need to determine the radius of the circle using its circumference. Then we calculate the area of the full circle and divide it by 4, since a quadrant is one-fourth of the circle. Let’s solve step by step:

Circumference of the circle: The formula for the circumference of a circle is: C = 2 * π * r Here, the circumference C is given as 22 cm.

Substitute the value of C: 22 = 2 * π * r

Solving for r: r = 22 / (2 * π) Using π ≈ 22/7: r = 22 / (2 * 22/7) r = 22 * 7 / 44 r = 7/2 r = 3.5 cm

So, the radius of the circle is 3.5 cm.

Area of the full circle: The formula for the area of a circle is: A = π * r²

Substituting the value of r: A = (22/7) * (3.5)² A = (22/7) * 12.25 A = 38.5 cm²

The area of the full circle is 38.5 cm².

Area of the quadrant: A quadrant is one-fourth of the circle, so the area of the quadrant is: Area of quadrant = (1/4) * Area of full circle Area of quadrant = (1/4) * 38.5 Area of quadrant = 9.625 cm²

Final Answer: The area of the quadrant is 9.625 cm².