Question

formula of ring in maths​

Answer 1

Answer:

Therefore, the area of a circular ring = π(R + r) (R - r), where R and r are the radii of the outer circle and the inner circle respectively.

R is an abelian group under addition, meaning that:

(a + b) + c = a + (b + c) for all a, b, c in R   (that is, + is associative).

a + b = b + a for all a, b in R   (that is, + is commutative).

There is an element 0 in R such that a + 0 = a for all a in R   (that is, 0 is the additive identity).

For each a in R there exists −a in R such that a + (−a) = 0   (that is, −a is the additive inverse of a).

R is a monoid under multiplication, meaning that:

(a · b) · c = a · (b · c) for all a, b, c in R   (that is, · is associative).

There is an element 1 in R such that a · 1 = a and 1 · a = a for all a in R   (that is, 1 is the multiplicative identity).[5]

Multiplication is distributive with respect to addition, meaning that:

a ⋅ (b + c) = (a · b) + (a · c) for all a, b, c in R   (left distributivity).

(b + c) · a = (b · a) + (c · a) for all a, b, c in R   (right distributivity).

Answer 2

$\huge\bold{\color{maroon}{\fbox{Answer}}} \\ \\ Area \: of \: ring \\ = \pi \: R {}^{2} - \pi \: r { }^{2} \\ = \pi(R {}^{2} - r {}^{2} ) \\ = \pi \: ( R+ r)(R - r)$