Step-by-step explanation:
The area of a circle is calculated using the formula: πr^2
The circumference of a circle is calculated using: 2πr
We are given 8 questions, So by addressing them individually
1) Area of Circle 1:
Radius = r = 12 mi
Total angle in a circle = 360°
Given angle = 90
Ratio 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 in
Total angle in a circle = 360°
Given angle = 315
Ratio 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 km
Total angle in a circle = 360°
Given angle = 270
Ratio 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 f
4) Area of Circle 4:
Radius = r = 6 km
Total angle in a circle = 360°
Given angle = 270
Ratio 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 f
5) Circumference of Circle 1:
Radius = r = 12 mi
Total angle in a circle = 360°
Given angle = 90
Ratio 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 f
6) Circumference of Circle 2:
Radius = r = 19 in
Total angle in a circle = 360°
Given angle = 315
Ratio 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 f
7) Circumference of Circle 3:
Radius = r = 15 km
Total angle in a circle = 360°
Given angle = 270
Ratio 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 f
8) Circumference of Circle 4:
Radius = r = 6 km
Total angle in a circle = 360°
Given angle = 270
Ratio 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
