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LUCKY_DIMON [66]
3 years ago
8

What is the exact area and circumference?

Mathematics
1 answer:
Rudik [331]3 years ago
6 0

Answer:

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

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