Answer:
Total area of the gray sections of the target is 678 square inches.
Step-by-step explanation:
Given :
Three concentric circles and we have to find the total area of the gray sections.
Area of white circle having radius 1 foot.
⇒ Area of the white circle - Area of the smaller gray circle.
⇒ [tex]\pi R^2-\pi r^2[/tex]
⇒ [tex]\pi (R^2-r^2)[/tex]
⇒ [tex]\pi (12^2-6^2)[/tex] ...1 foot = 12 inches and 0.5 foot = 6 inches
⇒ [tex]3.14(144-36)[/tex]
⇒ [tex]3.14(108)[/tex]
⇒ 339.12 square inches
The total area of the gray sections is the area of the bigger gray circle minus the area of the white circle.
Total area of the gray sections:
⇒ [tex]\pi R^2 - 339.12[/tex]
⇒ [tex]3.14(18^2) -339.12[/tex] ....where 1.5 foot = 18 inches
⇒ [tex]1017.36-339.12[/tex]
⇒ [tex]678.24[/tex] square inches.
≅ 678 square inches.
The total area of the gray sections of the target, to the nearest square inch is 678.
Option C is the right choice.
