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
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)