Question

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

Answer 1

Given:

✰ Radii of two circles are 19 cm and 9 cm respectively.

✰ Circumference of a circle is equal to the sum of the circumferences of the two circles.

To find:

✠ The radius of a circle which has circumference of a circle is equal to the sum of the circumferences of the two circles.

Solution:

Let's understand the concept first! First we will find the circumference of one circle and then the circumference of the other circle, by using the formula of circumference of circle. Putting the values in the formula and then doing the required calculations. After that we know circumference of a circle is equal to the sum of the circumferences of the two circles, so we will add the circumferences of both the circles, then we will find the radius of a circle by using the formula of circumference.

Let's find out...✧

✭ Circumference of circle = 2πr ✭

Putting the values in the formula, we have:

⤳Circumference of 1st circle = 2 × π × 19

⤳Circumference of 1st circle = 38π cm

⤳Circumference of 2nd circle = 2 × π × 9

⤳Circumference of 2nd circle = 18π cm

We know that the circumference of a required circle is equal to the sum of the circumferences of the two circles.

⤳ Circumference of a required circle = Circumference of 1st circle + Circumference of 2nd circle

⤳ Circumference of a required circle = 38π + 18π

⤳ Circumference of a required circle = 56π cm

✭ Circumference of circle = 2πr ✭

Here,

r is the radius of a required circle.

Putting the values in the formula, we have:

➤ 56π = 2 × π × r

➤ 56 = 2 × r

➤ r = 56/2

➤ r = 28 cm

∴ The radius of the required circle = 28 cm

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