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Mathematics

Find the circumference of a circle whose area is 1386 cm2.

Area Trapezium Polygon

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Answer

Let r be the radius of the circle.

The area of circle = 1386 cm2

As we know, the area of the circle = πr2

227×r2=1386r2=1386×722r2=970222r2=441r=441r=21 cm⇒ \dfrac{22}{7} \times r^2 = 1386\\[1em] ⇒ r^2 = \dfrac{1386 \times 7}{22}\\[1em] ⇒ r^2 = \dfrac{9702}{22}\\[1em] ⇒ r^2 = 441\\[1em] ⇒ r = \sqrt{441}\\[1em] ⇒ r = 21 \text{ cm}

Circumference of the circle = 2πr

=2×227×21=447×21=9247=132 cm= 2 \times \dfrac{22}{7} \times 21\\[1em] = \dfrac{44}{7} \times 21\\[1em] = \dfrac{924}{7}\\[1em] = 132 \text{ cm}

Hence, the circumference of the circle is 132 cm.

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