Final answer:
The area of the sector formed by the hands of the clock at 4:00 can be calculated using the formula for the area of a sector. The radius of the clock is equal to the length of the minute hand, and the angle formed by the hands at 4:00 is 120 degrees or 2/3 of a revolution. By plugging these values into the formula, the area of the sector is approximately 301.44 square inches.
Step-by-step explanation:
The area of the sector formed by the hands of the clock can be calculated using the formula:
Area = (θ/360) x πr^2
where θ is the angle formed by the hands of the clock, r is the radius of the clock, and π is the mathematical constant pi.
In this case, the minute hand of the clock is 12 inches long, which is the same as the radius of the clock. The angle formed at 4:00 is 120 degrees or 2/3 of a revolution. Therefore, the area of the sector can be calculated as:
Area = (2/3)(π * 12^2)
Area = 96π square inches
Using an approximation of π as 3.14, the area of the sector is approximately 301.44 square inches.