Answer:Step-by-step explanation:The area of a circle is calculated using the formula: πr^2The circumference of a circle is calculated using: 2πrWe are given 8 questions, So by addressing them individually1) Area of Circle 1:Radius = r = 12 miTotal angle in a circle = 360° Given angle = 90Ratio of given circle to complete circle = 90/360=> 1/4 Therefore, the circle 1 is 1/4 of the complete circle with r = 12. In this way, its area will be 1/4 of the complete circle.Hence Area = 1/4 (πr^2)=> 1/4 (π*12^2 )=> 1/4 (144π)=> 36π Hence option C 2) Area of Circle 2:Radius = r = 19 inTotal angle in a circle = 360° Given angle = 315Ratio of given circle to complete circle = 315/360=> 7/8 Therefore, the circle 2 is 7/8 of the complete circle with r = 19. In this way, its area will be 7/8 of the complete circle.Hence Area = 7/8 (πr^2)=> 7/8 (π*19^2 )=> 7/8 (361π)=> 315.8π Hence answer is not provided that is option f 3) Area of Circle 3:Radius = r = 15 kmTotal angle in a circle = 360° Given angle = 270Ratio of given circle to complete circle = 270/360=> 3/4 Therefore, the circle 3 is 3/4 of the complete circle with r = 15. In this way, its area will be 3/4 of the complete circle.Hence Area = 3/4 (πr^2)=> 3/4 (π*15^2 )=> 3/4 (225π)=> 168.75π Hence answer is not provided that is option f4) Area of Circle 4:Radius = r = 6 kmTotal angle in a circle = 360° Given angle = 270Ratio of given circle to complete circle = 90/360=> 3/4 Therefore, the circle 4 is 3/4 of the complete circle with r = 6. In this way, its area will be 3/4 of the complete circle.Hence Area = 3/4 (πr^2)=> 3/4 (π*6^2 )=> 3/4 (36π)=> 27π Hence answer is not provided that is option f5) Circumference of Circle 1:Radius = r = 12 miTotal angle in a circle = 360° Given angle = 90Ratio of given circle to complete circle = 90/360=> 1/4 Therefore, the circle 1 is 1/4 of the complete circle with r = 12. In this way, its circumference will be 1/4 of the complete circle. In addition to that, its boundary will include the radius of both sides to make it a close shape.Hence Circumference = 1/4 (2πr) + 2r=> 1/4 (2π12) + 2*12=> 1/4 (24π) + 24=> 6π + 24 Hence answer is not provided that is option f6) Circumference of Circle 2:Radius = r = 19 inTotal angle in a circle = 360° Given angle = 315Ratio of given circle to complete circle = 315/360=> 7/8 Therefore, the circle 2 is 7/8 of the complete circle with r = 19. In this way, its circumference will be 7/8 of the complete circle. In addition to that, its boundary will include the radius of both sides to make it a close shape.Hence Circumference = 7/8 (2πr) + 2r=> 7/8 (2π19) + 2*19=> 7/8 (38π) + 38=> 33.25π + 38 Hence answer is not provided that is option f7) Circumference of Circle 3:Radius = r = 15 kmTotal angle in a circle = 360° Given angle = 270Ratio of given circle to complete circle = 270/360=> 3/4 Therefore, the circle 3 is 3/4 of the complete circle with r = 15. In this way, its circumference will be 3/4 of the complete circle. In addition to that, its boundary will include the radius of both sides to make it a close shape.Hence Circumference = 3/4 (2πr) + 2r=> 3/4 (2π19) + 2*15=> 3/4 (38π) + 38=> 28.5π + 38 Hence answer is not provided that is option f8) Circumference of Circle 4:Radius = r = 6 kmTotal angle in a circle = 360° Given angle = 270Ratio of given circle to complete circle = 270/360=> 3/4 Therefore, the circle 3 is 3/4 of the complete circle with r = 6. In this way, its circumference will be 3/4 of the complete circle. In addition to that, its boundary will include the radius of both sides to make it a close shape.Hence Circumference = 3/4 (2πr) + 2r=> 3/4 (2π6) + 2*6=> 3/4 (12π) + 12=> 9π + 12 Hence answer is not provided that is option f