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11Alexandr11 [23.1K]
3 years ago
14

The area of one of the smaller circles is 8/ in². Find the area of the shaded region.

Mathematics
1 answer:
Ksju [112]3 years ago
8 0

Answer:

Area of shaded region = 16π in² (D)

Step-by-step explanation:

The question is incomplete without the diagram if the circles. Find attached the diagram used in solving the question.

Area of the smaller circle = 8π in²

Area of a circle = πr²

πr² = 8π

r² =8

r = √8 = 2√2

From the diagram, there are two smaller circles in a bigger circle.

The radius of the bigger circle (R) is 2times the radius of the smaller circle (r)

R = 2r

Area of bigger circle = πR²

= π×(2r)² =   π×(2×2√2)²

= π×(4√2)² = π×16×(√2)²

Area of bigger circle = π×16×2

Area of bigger circle = 32π in²

Since there are two smaller circles in a bigger circle

Area of shaded region = Area of bigger circle -2(area of smaller circles)

Area of shaded region = 32π in² - 2(8π in²)

Area of shaded region = 32π in² - 16π in²

Area of shaded region = 16π in²

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Which equation represents a circle that contains the point (-5, -3) and has a center at (-2, 1)?
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The equation (x + 2)² + (y - 1)² = 25 represents a circle that contain the point (-5 , -3) and has a center at (-2 , 1)

Step-by-step explanation:

The equation of a circle of center (h , k) and radius r is:

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- Substitute the values of h , k , r² in the equation of the circle

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∴ (x + 2)² + (y - 1)² = 25

The equation (x + 2)² + (y - 1)² = 25 represents a circle that contains

the point (-5 , -3) and has a center at (-2 , 1)

Learn more:

You can learn more about the equation of the circle in brainly.com/question/9510228

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