Math, asked by sta023shwetanegic7, 3 days ago

The area of the Ring between two concentric circle is 3168cm² find the radii of the two circles if their sum is 42 and the difference is 28 cm.

Answers

Answered by yogeshgangwar044
2

Answer:

The radii will be (33 cm, 9 cm) or (32 cm, 4 cm)

Step-by-step explanation:

Let the radius of two circles be x and y respectively.

It is given that, Area of the ring between two concentric circles = 3168 cm²

Area of the ring between two concentric circles = π(x² - y²)

3168 = π (x + y)(x - y)              Using identity a² - b² = (a + b) (a - b)

It is also given that x + y = 42. Putting this in above equation we get,

3168 = π (42) (x - y)

x- y = 24       ____ 1)

And we know that x + y = 42      ____2)

Adding eq. 1 and eq. 2, we get

x - y + x + y = 24 + 42

2x = 66

x = 33 cm

So, 33 - y = 24

y = 9 cm

If we put the value of x - y = 28 in 3168 = π (x + y)(x - y), we get

3168 = π (x + y) × 28

x + y = 36   _____ 3)

x - y = 28   _____ 4)

Adding eq. 3 and eq. 4

x + y + x - y = 36 + 28

2x = 64

x = 32 cm

32 - y = 28

y = 4 cm.

So, the radii will be (33 cm, 9 cm) or (32 cm, 4 cm)

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