Question

what is the sector area created by the hands of a clock with a radius of 9 inches when the time is 4:00?○ $6.75\pi$ $in.^2$○ $20.25\pi$ $in.^2$○ $27\pi$ $in.^2$○ $81\pi$ $in.^2$

Explanation:

Step1: Find clock sector fraction

A clock is 360°, divided into 12 equal parts. At 4:00, the hour hand is at 4, minute at 12, so they span 4 parts.
Fraction = $\frac{4}{12} = \frac{1}{3}$

Step2: Calculate full clock area

Use circle area formula $A = \pi r^2$, $r=9$.
Area = $\pi \times 9^2 = 81\pi$

Step3: Compute sector area

Multiply full area by fraction.
Sector Area = $81\pi \times \frac{1}{3}$

Answer:

27π in.² (Option C)