A sector of 120 degrees cut out from a circle has an area of 66/7 sq cm. Find the radius of the circle (in cm), assuming pi = 22/7.

Introduction / Context:This question tests the area of a sector of a circle. A sector is a fraction of a full circle based on the central angle. If the central angle is theta degrees, then sector area = (theta/360)*pi*r^2. Here theta is 120 degrees, so the sector is exactly one-third of the full circle. With the sector area known, we can set up an equation in r^2 and solve for the radius. Using pi = 22/7 is intended to keep the arithmetic exact and clean.

Given Data / Assumptions:

• Sector angle theta = 120 degrees
• Sector area = 66/7 sq cm
• pi = 22/7
• Sector area formula: (theta/360)*pi*r^2

Concept / Approach:Use: (120/360)*pi*r^2 = 66/7. Simplify 120/360 to 1/3, substitute pi = 22/7, solve for r^2, then take square root to get r in cm.

Step-by-Step Solution: (120/360) = 1/3 (1/3) * (22/7) * r^2 = 66/7 Multiply both sides by 3: (22/7)*r^2 = 198/7 Cancel /7: 22*r^2 = 198 r^2 = 198/22 = 9 r = sqrt(9) = 3 cm

Verification / Alternative check:Full circle area would be 3 times sector area (since 120 degrees is 1/3 of 360): full area = 3*(66/7) = 198/7. Using r=3 gives pi*r^2 = (22/7)*9 = 198/7. Perfect match confirms the radius.

Why Other Options Are Wrong: 1 cm and 2 cm give much smaller areas because area grows with r^2. 4 cm and 6 cm produce areas larger than 66/7 for the 120-degree sector.

Common Pitfalls:Using theta as 120 radians (wrong), forgetting the (theta/360) factor, or not squaring r properly when rearranging.

Final Answer:The radius of the circle is 3 cm.