Question

the perimeter of a new circle is equal to the sum of the areas of two circle of radii 3cm and 5cm then the radius of the new circle is ​

Answer 1

perimeter = 3.14 (9+25)

3.14×2r =3.14×34

r=17

Answer 2

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: SOLUTION \: \: \red{ \mid}}}}}}}}$

$\underline{ \underline {\bold{ \: \: GIVEN \: \: } }} \to\\ \\ \bold{Radius \: \: of \: \: the \: \: first \: \: circle \:, \: r_1 = 3 \: \: cm} \\ \\ \bold{ \therefore \: \: Area \: \: of \: \: the \: \: circle \:, \: A_1= \pi \: {r_1}^{2}} \\ \\ \bold{ = [ \pi \times {(3)}^{2}] \: \: sq.cm} \\ \\ \bold{ = 9\pi \: \: sq.cm}$


$\bold{Again} \\ \\ \bold{Radius \: \: of \: \: the \: \: second \: \: circle \:, \: r_2 = 5 \: \: cm} \\ \\ \bold{ \therefore \: \: Area \: \: of \: \: the\: \: circle \: ,\: A_2 = \pi \:{r_2}^{2}} \\ \\ \bold{ =[ \pi \: \times { (5) }^{2} ] \: \:sq. cm} \\ \\ \bold{ = 25 \pi \: \: cm}$

$\bold{ \therefore \: \: Sum \: \: the \: \: area \: \: of \: \: the \: \: two \: \: circle}\\ \\ \bold{ = A_1 + A_2} \\ \\ \bold{ =9\pi \: \: cm + 25\pi \: \: cm} \\ \\ \bold{ = 34\pi \: \: sq.cm}$

$\bold{Let,} \\ \\ \bold{Radius \: \: of \: \: the \: \: new \: \: circle = R} \\ \\ \bold{ \therefore \: \: Perimeter \: \: of \: \: the\: \: new \: \: circle \:, \: S = 2\pi \: R} \\ \\ \underline{\bold{ \: \: According \: \: To \: Question \: \: }} \\ \\ \bold{2\pi \: R = 34 \pi} \\ \\ \bold{ \Longrightarrow \: \: 2R = 34} \\ \\ \bold{ \Longrightarrow \: \: R = \frac{34}{2} } \\ \\ \bold{ \Longrightarrow \: \: R = 17}$

$\bold{So ,\: \: Radius \: \: of \: \: the \: \: new \: \: circle \: , \: R = \underline{\red{17 \: cm}}}$