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