Find the area of a quadrant of a circle whose circumference is 66 cm.
86.625 cm²
Explanation
To find the area of a quadrant, we first need the radius of the circle. The circumference formula (2πr) is used to find the radius from the given circumference. Once the radius is found, the area of the full circle is calculated using πr². As stated in the text, a quadrant is a quarter circular disc, meaning its area is (90/360)th or 1/4 of the total area of the circle. Using the approximation 22/7 for π as directed by the textbook exercises, we compute the final area.
Solution Steps
Step 1: Find the radius of the circle. Given, Circumference = 66 cm. Circumference = 2πr ⇒ 2 × (22/7) × r = 66 ⇒ (44/7) × r = 66 ⇒ r = () / 44 ⇒ r = 462 / 44 = 10.5 cm
Step 2: Find the area of the circle. Area of the circle = πr² = (22/7) × (10.5)² = (22/7) × 110.25 = 346.5 cm²
Step 3: Find the area of the quadrant. Area of a quadrant = (1/4) × Area of the circle = (1/4) × 346.5 = 86.625 cm²