Question

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 circumference of the two circle

Answer 1

The radius of first circle is 19 cm
So circumference will be =2πr
=2×22÷7×19=396÷7 cm
The radius of second circle is 9 cm
So circumference will be =2πr=2×22÷7×9=836÷7 cm
The sum of the circumference of the two circles will be =(396÷7)+(836÷7)=1232÷7=176 cm
The required circle's circumference =2πr=176 cm
r = (176÷2π)=176÷(2×22÷7)=(176×7)÷(2×22)
=28 cm
Therefore the required circle's radius is 28 cm
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Answer 2

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

We've to find out the radius of the circle which has circumference equal to the sum of the circumference of the two circle.

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

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

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

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

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

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

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$\star$ Circumference of third Circle = Circumference of 1st circle + circumference of 2nd circle.

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

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