A wall clock is equally divided into 12 sections. If the clock reads 8:00 and has a diameter of 12.5 inches, find the area of the smaller sector formed by the minute and hour hands.
Accepted Solution
A:
Answer: Our required area would be 11.93 sq. inches.Step-by-step explanation:Since we have given that Number of sections = 12Angle formed in every 5 minutes is given by[tex]\dfrac{360}{12}=30^\circ[/tex]Diameter = 12.5 inchesRadius = [tex]\dfrac{12.5}{2}=6.25\ inches[/tex]Area of the smaller sector formed by the minute and hour hands would be [tex]\dfrac{\theta}{360^\cir}\times \pi r^2\\\\=\dfrac{30}{360}\times \dfrac{22}{7}\times 6.75\times 6.75\\\\=11.93\ sq.\ inches[/tex]Hence, our required area would be 11.93 sq. inches.