Question

The radii of two circle 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

I'll give you the steps you solve the problem. Okay.
#Find circumference of both the circles using formula circumference=2πR (R=Radius)
#Add the values.
#Now find the radius of the circle whose circumference is the sum of the values obtained using the given formula.

I hope this helps you.

Answer 2

Given

• Radius of 1st circle=19 cm
• Radius of 2nd circle=9 cm

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

$\underline{\:\large{\textit{1. \sf Circumference of 1st circle :}}} \\ </p><p></p><p> </p><p></p><p>\star \ \boxed{\sf{\pink{ Circumference \: = \: 2 \pi r}}}⋆ \\ </p><p></p><p> </p><p> </p><p></p><p>\begin{gathered}:\implies\sf Circumference = 2 \pi \Big( 19 \Big) \\\\\\:\implies\boxed{\frak{\pink{ \: 38 \pi \: }}}\end{gathered} \\ </p><p> </p><p></p><p>\underline{\:\large{\textit{1. \sf Circumference of 2nd circle :}}} \\ </p><p></p><p> </p><p> </p><p></p><p>\begin{gathered}:\implies\sf Circumference = 2 \pi \Big( 9 \Big) \\\\\\:\implies\boxed{\frak{\pink{\: 18 \pi \; }}}\end{gathered} \\ </p><p></p><p>$

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

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀

• Circumference of third Circle = Circumference of 1st circle + circumference of 2nd circle.

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

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

.