Question

Find the radius of the circle whose area is equal to the sum of the area of three circle with radii 2, 5 6 cm​

Answer 1

Given :

• The circle whose area is equal to the sum of the area of three circle with radii 2, 5, 6 cm.

To find :

• Radius of the big circle.

Solution :

• Radii of 1st circle = 2 cm
• Radii of 2nd circle = 5 cm
• Radii of 3rd circle = 6 cm

Formula Used :-

${\boxed{\bold{Area\:of\: circle=\pi\:r^2}}}$

★ $\sf{Area_{\:\:1st\: circle}=\pi\times\:2^2\:cm^2}$

$\to\sf{Area_{\:\:1st\: circle}=4\pi\:cm^2}$

★$\sf{Area_{\:\:2nd\: circle}=\pi\times\:5^2\:cm^2}$

$\to\sf{Area_{\:\:2nd\: circle}=25\pi\:cm^2}$

★$\sf{Area_{\:\:3rd\: circle}=\pi\times\:6^2\:cm^2}$

$\to\sf{Area_{\:\:3rd\: circle}=36\pi\:cm^2}$

Sum of the area of 3 circles ,

= ( 4π + 25π + 36π) cm²

= 65π cm²

Consider,

• Radius of the big circle = R cm

${\underline{\sf{According\:to\: the\: question:-}}}$

$\to\sf{\pi\:R^2=65\pi}$

$\to\sf{R^2=65}$

$\to\sf{R=\sqrt{65}}$

$\to\sf{R=8.06}$

Therefore, radius of the big circle is 8.06 cm ( approx) .