Respuesta :
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Given Information
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Area of 2 circles = 80π m²
One radius is twice as long as the other
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Define Radius
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Let one of the radius be x
Radius₁ = x
Radius₂ = 2x ← (Because it is twice as long)
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Formula
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Area of circle = πr²
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Substitute the radius into the formula
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Area of big circle + Area of small circle = πr₁² + πr₂²
Area of big circle + Area of small circle = πx² + π(2x)²
πx² + π(2x)² = 80π
πx² + π4x² = 80π
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Divide by π through
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x² + 4x² = 80
5x² = 80
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Divide by 5 through
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x² = 80 ÷ 5
x² = 16
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square root both sides
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x = √16
x = 4 (-4 is rejected, because length cannot be negative)
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Find Radius
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Radius₁ = x = 4m
Radius₂ = 2 = 2(4) = 8m
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Answer: The radius of the smaller circle is 4m and the radius of the bigger circle is 8m.
----------------------------------------------------------------------------------------
Given Information
----------------------------------------------------------------------------------------
Area of 2 circles = 80π m²
One radius is twice as long as the other
----------------------------------------------------------------------------------------
Define Radius
----------------------------------------------------------------------------------------
Let one of the radius be x
Radius₁ = x
Radius₂ = 2x ← (Because it is twice as long)
----------------------------------------------------------------------------------------
Formula
----------------------------------------------------------------------------------------
Area of circle = πr²
----------------------------------------------------------------------------------------
Substitute the radius into the formula
----------------------------------------------------------------------------------------
Area of big circle + Area of small circle = πr₁² + πr₂²
Area of big circle + Area of small circle = πx² + π(2x)²
πx² + π(2x)² = 80π
πx² + π4x² = 80π
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Divide by π through
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x² + 4x² = 80
5x² = 80
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Divide by 5 through
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x² = 80 ÷ 5
x² = 16
----------------------------------------------------------------------------------------
square root both sides
----------------------------------------------------------------------------------------
x = √16
x = 4 (-4 is rejected, because length cannot be negative)
----------------------------------------------------------------------------------------
Find Radius
----------------------------------------------------------------------------------------
Radius₁ = x = 4m
Radius₂ = 2 = 2(4) = 8m
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Answer: The radius of the smaller circle is 4m and the radius of the bigger circle is 8m.
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