Question

22
Unless stated otherwise, use a
7
The radii of two circles are 19 cm and 9 em respectively,
Find the radius of the circle which has circumference equal
to the sum of the circumferences of the two circles.
om ond om reenectively. Find​

Answer 1

Given:

• Radius of 1st circle, r₁ = 9 cm
• Radius of 2nd circle, r₂ = 19 cm

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━

✇ Let the radius of required circle formed be r cm

⠀

$\underline{\textsf{\textbf{According\:to\:question\::}}}$

Circumference of required circle = Sum of circumference of two circles

⠀

$\underline{\:\bigstar\:{\textsf{Circumference\:of\:smaller\:circle\::}}}$

$:\implies\sf 2 \pi r_1$

$:\implies\sf 2 \pi \times 9$

$:\implies\sf 18 \pi$

$\underline{\:\bigstar\:{\textsf{Circumference\:of\:larger\:circle\::}}}$

$:\implies\sf 2 \pi r_2$

$:\implies\sf 2 \pi \times 19$

$:\implies\sf 38 \pi$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━

Now,

⠀

Circumference of required circle = Sum of circumference of two circles

⠀

$\dashrightarrow\sf 2 \pi r = 2 \pi r_1 + 2 \pi r_2$

$\dashrightarrow\sf 2 \pi r = 18 \pi + 38 \pi$

$\dashrightarrow\sf 2 \pi r = 56 \pi$

$\dashrightarrow\sf r = \dfrac{56 \pi}{2 \pi}$

$\dashrightarrow{\underline{\boxed{\sf{r = 28\;cm}}}}\;\bigstar\;$

$\therefore\;{\underline{\sf{Hence,\; Radius\;of\;new\;circle,\;r\;is\; \bf{28\;cm}.}}}$

Answer 2

◓◓◓◓◓◓◓◓◓◔◔❃❃◖◔◗ 　◓◔◕❃❃❃✤✤❁✾❁✾❁✤❁✤❁✾◗ 　✤✤✿✿✥★★★★★❖✥✥★<————««<————««<————««

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.