Respuesta :
Answer: Our required area would be 11.93 sq. inches.
Step-by-step explanation:
Since we have given that
Number of sections = 12
Angle formed in every 5 minutes is given by
[tex]\dfrac{360}{12}=30^\circ[/tex]
Diameter = 12.5 inches
Radius = [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.
Answer:
The area of the sector is 81.8 square inches.
Step-by-step explanation:
The wall clock has handas that move 360°. So, if it's equally distributed then, we can divide
[tex]\frac{360\°}{12}= 30\°[/tex]
Thich means that during each interval of hour, the hands move 30°.
So, if the wall clock is showing 8 o'clock, than one hand is pointing 12, which is gonna be the reference point 0°. The hour hand would be at number 8, which forms an angle of
[tex]8(30\°)=240 \°[/tex]
Now, to find the circular sector area we used the following formula
[tex]A= \frac{\theta}{360 \°} \times \pi r^{2}[/tex]
Where [tex]\theta = 240 \°[/tex] and [tex]r=\frac{12.5 in}{2}= 6.25 in[/tex], because the radius is defined as half the diameter.
Replacing all these values and [tex]\pi =3.14[/tex], we have
[tex]A= \frac{240\°}{360 \°} \times (3.14) (6.25in)^{2}=81.8 in^{2}[/tex]
Therefore, the area of the smaller sector formed by the minute and hour hands is 81.8 square inches.
