Question

the radius of two circles are 8cm and 6cm respectively find the radius of the circle having its area equal to the the sum of the areas of the two circles. with diagram​

Answer 1

Answer:

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Answer 2

Given :-

• the radius of two circles are 8cm and 6cm respectively find the radius of the circle having its area equal to the the sum of the areas of the two circles.

To find :-

• Radius of 1st circle = r² = 8 cm.
• Radius of 2nd circle = r² = 6 cm.

Let the redius of required circle = r cm.

• According to question

Area of required circle = sum of the area of both the circles.

Solution :-

${\bf{Area~of~the~first~circle}}$ = πr²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= π( 8 )²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= π(8 × 8)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\boxed{\bf\red{64π}}$

${\bf{Area~of~the~second~circle}}$ = πr²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= π( 6 )²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= π(6 × 6 )

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\boxed{\bf\green{36π}}$

Hence,

• The area of first circle is ${\bf\underline{64π}}$
• The second area is ${\bf\underline{36π}}$