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

the first circle area is 8cm squ

second circle area is 6c squ

Answer 2

Given :-

• Radius of 1st Circle = 8cm
• Radius of 2nd Circle = 6cm
• The 3rd circle is having area equal to the sum of the areas of the two circles.

To Find :-

• Radius of the 3rd Circle.

Solution :-

⟾ Radius of 1st Circle = 8cm

• Area of 1st Circle = πr²
• Area of 1st Circle = π × (8)²
• Area of 1st Circle = π × 8 × 8
• Area of 1st Circle = 64π

⠀

⟾ Radius of 2nd Circle = 6cm

• Area of 2nd Circle = πr²
• Area of 2nd Circle = π × (6)²
• Area of 2nd Circle = π × 6 × 6
• Area of 2nd Circle = 36π

⠀

⟾ Total Area of Circles :

• Total Area = 1st + 2nd circle's area
• Total Area = 64π + 36π
• Total Area = 100π

⠀

⟾ Required Radius of 3rd Circle :

• Area of 3rd Circle = Total Area
• πr² = 100π
• r² = 100
• r = √100
• Radius = 10cm

⠀

∴ Required Radius of 3rd Circle is 10cm

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★ Additional Info :

Formulas Related to Circle:

• Circumference of Circle = 2πr
• Area of Circle = πr²
• Diameter of Circle = 2r
• Radius of Circle = D/2

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