Question

the area of the region between two concrete circle is 3168 CM square find the radius of the two circle first their sum is 42 cm and their difference is 28 CM​

Answer 1

Answer:

Question is not clear, if the sum and difference of radii are given, the radii can be solved. without using info regarding area of region.

R1 + R2 = 42

R1 - R2 = 28

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2R1 = 70

R1 = 35

R2 = 7

However, I feel this question is combination of two questions to find radii where

1. area of region and sum of radii are give

2. area of region and difference of radii are given

let us try solving 1

let smaller radius be r

bigger radius = 42 - r

area of region = 3168

π{42-r)^2 - r^2) = 3168

(1764 + r^2 - 84r - r^2) = 3168*7/22. (π = 22/1)

1764 - 84r = 1008

84r = 1764 - 1008

84r = 756

r = 756/84

r= 9

bigger radius = 42 - r = 42 - 9 = 33

hence radii are 9 and 33

Q2.

let smaller radius be r

bigger radius = r + 28

area of region = 3168

π((r+28)^2 - r^2) = 3168

(r^2 + 56r + 784 - r^2) = 3168*7/22

56r + 784 = 1008

56r = 1008 - 784

56r = 224

x = 224/56

x= 4

bigger radius = 28+4 = 32

hence radii are 4 and 32