Question

Unless stated otherwise, use it 22/7

1. The radii 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.
please answer this​

Answer 1

Step-by-step explanation:

• Let the radius of required circle =r cm
• Radius of 1st circle r

1=9 cm

• Radius of 2nd circle r

2=19 cm

• As per the question

Circumference of the required circle = Sum of circumference of two circles

Circumference of small circle =2πr

1

=2π×9

=18π

Circumference of small circle =2πr

2

=2π×19

=38π

Now,

Circumference of the required circle = Sum of circumference of two circles

2πr=18π+38π

2πr=58π

r=

2π

56π

r=28 cm

Hence, radius of new circle is 28 cm

Hope it will help you ❤ plz support me

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

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

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