What is the radius of a circle if area of sector is 5π cm^2 and the central angle of sector is 100 degrees.
100° makes 5π cm²
360° makes (360÷100) 5π cm²
hence area of circle is 3.6 x 5π cm²
since area of circle = π(radius)²
3.6 x 5π = π(radius)²
radius = √((3.6 x 5π)÷π) = √18
radius = 4.243
πr²(100/360) = 5π => r² = 18 => r = 3√2 cm
The area of the entire circle is 3.6 x 5π cm², so the radius is √((3.6 x 5π)/π) = √(3.6 x 5) = 4.243 cm.
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Verified answer
100° makes 5π cm²
360° makes (360÷100) 5π cm²
hence area of circle is 3.6 x 5π cm²
since area of circle = π(radius)²
3.6 x 5π = π(radius)²
radius = √((3.6 x 5π)÷π) = √18
radius = 4.243
πr²(100/360) = 5π => r² = 18 => r = 3√2 cm
The area of the entire circle is 3.6 x 5π cm², so the radius is √((3.6 x 5π)/π) = √(3.6 x 5) = 4.243 cm.