Question

Show the mapping : 2
() → 2
() ℎ
(, ) = ( − , + ) is an isomorphism on 2
().

Answer 1

Answer:

Given-

Radius of Inner Circle = 5 units

Radius of Outer Circle= 7 units

To Find-

(i) Area of Outer Circle

(ii) Diameter of Inner Circle

Solution-

(i)Area of Outer Circle

Using Formula,

Area of Circle = πr^2r

2

\implies⟹ \frac{22}{7}×

7

22

× 7^27

2

\quad\quad (Radius,outer= 7 units)

\implies⟹ \frac{22}{\cancel{7}}× \cancel{7} × 7

7

22

×

7

×7

\implies⟹ 22×7

\implies⟹ 154

\therefore \sf\pink{Area\:of Outer\:Circle\:= 154\: sq \:units}∴AreaofOuterCircle=154squnits

______________________________

(ii)Diameter of Inner Circle

Using formula,

Diameter = 2 × radius

\implies Diameter= 2× 5⟹Diameter=2×5

\therefore \sf\red{Diameter= 10 units}∴Diameter=10units