Question

find the cir circumference of a circle whose area is equal to the sum of areas of two circles of radii 12cm and 5cm​

Answer 1

$\sf\large\pink{\underline{\underline{ \: Answer: \: }}}$

Given:

• Radii (Circles) = 12cm and 5cm

To Find:

• Circumference of Circle?

Formula Used:

$\\ \bullet{\boxed{\sf{ πr^2}}}$

Solution:

Firstly, We have to Find the areas of that Two small circles;

First Small Circle;

Area = πr² $\: \: \:$ [ r = 12cm]

= 22/7 × 12 × 12

= 452.57 cm²

Second small circle;

Area = πr² $\: \: \:$ [ r = 5 cm]

= 22/7 × 5 × 5

= 78.5 cm²

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Sum of Areas of the Circles:-

= 452.57 + 78.5

= 531.07 cm²

:- Area of Big Circle is equal to the sum of Areas of two small circles.

Area of Big Circle = Area of Small Circle

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Now,

We have to find the radius of Big Circle;

Area of Circle = πr²

531.07 = 22/7 × r²

531.07 × 7/22 = r²

168.97 = r²

r = √168.97

r = 13 cm

So, The radius of Big Circle is 13 cm.

Again ,

We have to Find Circumference of Big Circle;

Circumference of Circle = 2πr

= 2 × 22/7 × 13

= 81.64 cm

Hence,

The Circumference of Circle is 81.64 cm.

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