Question

2. The radii of two circles are 8 cm and 6 cm respectively. Find
the radius of the circle having area equal to the sum of the
areas of the two circles.
​

Answer 1

Explanation:

The radius of the first circle = 8 cm

Second radius of the circle = 6 cm

Area of a circle = pi R square

Then

Put the value of pi and R

22/7 and 8

22/7(8)squar

201.14

And second question

same to same first question

22/7(6) square

113.14cm

Answer 2

Solution:

We have,

$\bullet\:\:\textsf{Radius of first circle = \textbf{8 cm}} \\ </p><p>$

$\bullet\:\:\textsf{Radius of second circle = \textbf{6 cm}} \\ </p><p>$

Let the radius of first circle be $\r_1$ and second circle be $\r_2$ and required radius be 'r'.

$\bigstar \: \: \sf Area \: of \: first \: circle = \pi r_{1}^2$

$: \implies \sf Area \: of \: first \: circle = \pi ( {8})^{2}$

$: \implies \sf Area \: of \: first \: circle = 64\pi$

__________________________

$\bigstar \: \: \sf Area \: of \: second \: circle = \pi r_{2} ^2$

$: \implies \sf Area \: of \: second\: circle = \pi ( {6})^{2}$

$: \implies \sf Area \: of \: second\: circle = 36\pi$

_______________________

Now, we have to find area of required circle :

$\bigstar\:\: \boxed{\boxed{ \sf Area \: of \: required \: circle = Sum \: of \: the \: area \: of \: both \: the \: circles}}\:\:\bigstar \\ \\ </p><p>$

$\dag\:\: \boxed{ \sf Area \: of \: required \: circle =Area \: of \: first \: circle + Area \: of \: second \: circle </p><p> }\:\:\dag \\ \\ </p><p>$

$\dashrightarrow \: \: \sf Area \: of \: required\: circle =64\pi + 36\pi$

$\dashrightarrow \: \: \sf \cancel{\pi} r^{2} =100 \cancel{\pi }$

$\dashrightarrow \: \: \sf r^{2} =100$

$\dashrightarrow \: \: \sf r= \sqrt{100}$

$\dashrightarrow \: \: \underline{ \boxed{ \sf Radius = 10 \: cm}}$

$\therefore\:\underline{\textsf{Radius of required circle is \textbf{10 cm}}}.$