A clock's minute hand is 7 cm long. What area does it sweep in 15 minutes?

Introduction / Context:The tip of the minute hand traces a circle. In 15 minutes (a quarter hour), the hand sweeps a 90-degree sector. The question asks for the sector area.

Given Data / Assumptions:

• Radius r = 7 cm.
• Angle θ = 15/60 * 360 degrees = 90 degrees.

Concept / Approach:Sector area = (θ/360) * π * r^2. With θ = 90 degrees, this is one quarter of the circle area.

Step-by-Step Solution:Full circle area = π * 7^2 = 49π.Quarter of that = (1/4) * 49π = 12.25π cm^2.Using π ≈ 3.1416 gives ≈ 38.484 cm^2.

Verification / Alternative check:Compute with π = 22/7: (1/4)*49*(22/7) = (49/4)*(22/7) = 7*22/4 = 154/4 = 38.5 cm^2.

Why Other Options Are Wrong:25.6 and 44.0 are not consistent with the quarter-circle of radius 7; 77.0 is half-circle area using π ≈ 22/7 erroneously.

Common Pitfalls:Using diameter instead of radius; forgetting that 15 minutes is a quarter revolution.

Final Answer:38.5 cm^2