Question

the radii of 2 cirlcles is 9cm and 7cm respectively.Find the radius of circle having area equal to to the twice the sum of areas of two circles​

Answer 1

Given :-

• The radii of 2 cirlcles is 9cm and 7cm respectively.

To Find :-

• We have to find the radius of circle having area equal to the twice the sum of areas of two circles.

Solution :-

• Radius of first circle r₁ = 9 cm.
• Radius of second circle r₂ = 7 cm.

Let the Radius of required circle be r cm.

According to Question :-

→ Area of required circle = 2(Sum of the area of both the circles)

→ Area of required circle = 2(Area of first circle + Area of second circle)

→ Area of required circle =2(πr₁² + πr₂²)

→ Area of required circle = 2(π(9)² + π(7)²)

→ Area of required circle = 2(81π + 49π)

→ πr² = 2(130π)

→ πr² = 260π

Substracting π from both sides we get :

→ r² = 260

→ r = √260

→ r = 16.1 cm

Therefore,radius of required circle is 16.1 cm.

Answer 2

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: Question :- \: \star}}}}}$

The radii of 2 circles is 9cm and 7cm respectively.Find the radius of circle having area equal to to the twice the sum of areas of two circles.

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

$\underline{\boxed{\textsf{R = {\textbf{16. 1 cm}}}}} \qquad\qquad \bigg\lgroup\bold{Radius\ of \ the \ Circle} \bigg\rgroup$

$\Large{\underline{\underline{\bf{GiVen:-}}}}$

➹ The radii of 2 circles = 9 cm and 7cm

$\Large{\underline{\underline{\bf{Find:-}}}}$

✦ Find the radius of the circle .

$\Large{\underline{\underline{\bf{Solution:-}}}}$

We know from given

➹ Radius of the first circle r₁ = 9 cm.

➹Radius of the second circle r₂ = 7 cm.

So we consider radius = r cm.

Now ,

➹ Area of required circle = 2 ( Sum of the area of both the circles)

➹ Area of required circle = 2 ( Area of first circle + Area of second circle)

➹ Area of circle = 2(πr₁² + πr₂²)

➹ 2(π(9)² + π(7)²)

➹ 2(81π + 49π)

➹ πr² = 2(130π)

➹ πr² = 260π

Now ,

we have to subtract π from both sides

➹ πr² ( - π ) = 260π ( - π )

➹ r² = 260

➹ r = √260

→ r = 16.1 cm

$\Large{\boxed{\bf{\star \: R = 16 .1 cm \: \star}}}$

So Now ,

Therefore :- )

$\large{\boxed{\bold{Radius \:of\:circle\:=\:R\:=\:16.1\:cm}}}$