Question

The radius of a circle is greater than the radius of other circle by 3m.The sum of their area is 89 pie m square.Find the radius of each circle. ​

Answer 1

Given:-

• The radius of a circle is greater than the radius of other circle by 3 m.
• The sum of their area is 89 πm².

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To find:-

• Radius of each circle.

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Solution:-

Let,

• the radius of smaller circle be r.

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Then,

• radius of large circle = r + 3

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According to the question,

We know that,

→ Area of circle = πr²

→ πr² + π(r +3)² =  89π m²

→ π[r² + (r +3)²] =  89π

→ r² + (r +3)² = 89

→ r²  + r² +  6r + 9 = 89

→ 2r² +  6r + 9 - 89 = 0

→ 2r² +  6r - 80 = 0

→ r² +  3r  - 40 = 0

→ r² +  3r  - 40 = 0

→ r² +8r -5r - 40 = 0

→ r(r+8) - 5(r+8) = 0

→ (r-5)(r+8) = 0

→ r - 5 = 0  (or) r+8 = 0

→ r = 5 and r = -8

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Therefore,

• radius of smaller circle is 5 m.

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★ Radius of larger circle:-

→ r + 3

→ 5 + 3

→ 8cm

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Hence,

• Radius of smaller circle is 5m
• Radius of larger circle is 8m.