If the area of a circle is numerically equal to twice its circumference, then what is the diameter of the circle?

Given:

Area of circle = 2 × Circumference of circle …… (i)


Let the radius of the circle be ‘r’.


Then, the area of the circle = πr2


and the circumference of the circle = 2πr


Using (i), we have


πr2 = 2 × 2πr


πr2 = 4πr


r = 4 cm


∵ Diameter = 2 × radius


∴ Diameter = 2 × 4


= 8 cm


Hence, the diameter of the circle is 8 cm.


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