Question

The area of the ring between two concentric circles is 3168 cm2. Find the radil of the two circles if (i) their sum is 42 cm and (ii) their difference is 28 cm. ​

Answer 1

Answer:

Let radius by x and y (x > y)

pi*x² - pi*y² = 3168 [pi = 22/7]

x² - y² = 3168*7/22 = 1008

=> x² - y² = 1008 (or)

=> (x+y)(x-y) = 1008 [x²-y² = (x+y)(x-y)]

i) x+y = 42

=> 42(x-y) = 1008

=> (x-y) = 24

Solving (x-y) = 24 and (x+y) = 42, we get

=> x = 33 , and

=> y = 9

ii) x-y = 28

=> (x+y)*28 = 1008

=> (x+y) = 36

Solving (x-y) = 28 and (x+y) = 36, we get

=> x = 32 , and

=> y = 4

Hope it helps. Drop some Thanks if you found it helpful :)