Question

The radii of two circles are 19cm and 9cm. Fimd the radius of the circle, which has circumference equal to the sum of the circumferences of the two circles. ​

Answer 1

Step-by-step explanation:

Given:-

• Radii of two circles are 19cm and 9cm.

To Find:-

• The radius of the circle, which has circumference equal to the sum of the circumferences of the two circles.

Solution:-

$\sf Let \: the \: radius \: of \: new \: circle \: R$

$\sf Radius \: of \: the \: 1st \: circle \: (r_{1}) = 19cm$

$\sf Circumference \: of \: the \: 1st \: circle = 2\pi r_{1}$

$\sf = 2 \times \pi \times 19$

$\sf = 38 \pi$

$\sf Radius \: of \: the \: 2nd \: circle \: (r_{2}) = 19cm$

$\sf Circumference \: of \: the \: 2nd\: circle = 2\pi r_{2}$

$\sf = 2 \times \pi \times 9$

$\sf = 18 \pi$

Circumference of new circle = Circumference of (1st + 2nd) circle

$\sf = 38 \pi + 18 \pi$

$\sf = 56\pi$

$\sf Circumference\: of \: new \: circle = 2 \pi R$

$\sf \longrightarrow 2\pi R = 56\pi$

$\sf \longrightarrow 2R = 56$

$\sf \longrightarrow R = \dfrac{56}{2}$

$\sf \longrightarrow R = 28cm$

$\underline{\boxed{\sf \therefore Radius \: of \: new \: circle = 28cm}}$

Answer 2

ɢɪᴠᴇɴ :-

• The radii of 1st circle = 19 cm
• The radii of 2nd circle = 9 cm
• The sum of circumference of both the circles is equal to the circumference of 3rd circle.

ᴛᴏ ꜰɪɴᴅ :-

• The radius of the third circle.

ꜱᴏʟᴜᴛɪᴏɴ:-

we know,

The circumference of a circle is =$2\pi \times r$

So,

Circumference of 1st circle =$2\pi \times 19$

Circumference of 2nd circle =$2\pi \times 9$

Circumference of 3rd circle =$2\pi \times r$

Therefore,

The sum of the circumference of both the circles equals the circumference of the third circle.

$:\implies(2\pi \times 19) + (2\pi \times 9) = (2\pi \times r$

$:\implies \cancel {2\pi} \times (19 + 9) = \cancel {2\pi} \times r$

$:\implies r = 19 + 9$

$\begin{lgathered}\begin{lgathered}:\implies{\boxed{\frak{\pink{r=28 \;cm}}}}\;\bigstar\\ \\\end{lgathered}\end{lgathered}$

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