Question

The radius of two circles are 19 cm and 9 cm respectively.Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles

Answer 1

Here is your answer mate ☑☑☑

radius of first circle = 19 CM

circumference of first circle = 2πr1

radius of second circle = 9cm

circumference of second circle =2πr2

now

circumference of both circle=2πr1+2πr2

= 2π(r1+r2)

=2 ×22/7 (19+9)

=2×22/7 (28)

= 2×22×4

= 176cm

Since circumference of both circle = circumference of bigger circle

2πr = 176cm

2×22/7×r = 176cm

44/7 r =176

r= 176 × 7

—

44

r= 28 cm

Hence the radius of bigger circle= 28cm.

Answer 2

$\begin{gathered}\frak{ Given }\begin{cases}\sf{ Radius \ of \ 1st \ circle = 19 \ cm \:}\\\sf{ Radius \ of \ 2nd \ circle = 9 \ cm \:}\end{cases}\end{gathered}$

$\begin{gathered}\\\end{gathered}$

$\underline{\:\large{\textit{1. \sf Circumference of 1st circle :}}}$

$\star \ \boxed{\sf{\purple{ Circumference \: = \: 2 \pi r}}}⋆$

$\begin{gathered}:\implies\sf Circumference = 2 \pi \Big( 19 \Big) \\\\\\:\implies\boxed{\frak{\pink{ \: 38 \pi \: }}}\end{gathered}$

$\underline{\:\large{\textit{1. \sf Circumference of 2nd circle :}}}$

$\begin{gathered}:\implies\sf Circumference = 2 \pi \Big( 9 \Big) \\\\\\:\implies\boxed{\frak{\pink{\: 18 \pi \; }}}\end{gathered}$

Circumference of Both the circles is 38π & 18π.

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$\begin{gathered}\\\end{gathered}$

$\begin{gathered}:\implies\sf 2 \pi r = 38 \pi + 18 \pi \\\\\\:\implies\sf 2 \pi r = 56 \pi \\\\\\:\implies\sf r = \cancel\dfrac{56 \pi}{ 2 \pi}\\\\\\:\implies\underline{\boxed{\frak r = 28}}\end{gathered}$

$\therefore\:\underline{\textsf{Hence, required radius is \textbf{28 cm}}}.∴$