Question

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

Answer 1

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

Answer:

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Step-by-step explanation:

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