Question

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

Answer 1

Let the diameter of the required circle be d.
Now, Area of circle = 2 ⨯ Circumference of the circle 

`=> pi("d"/2)^2 =2(2pixxd/2)`

`=>(d/2)^2 =2"d"`

⇒ d² = 8d

⇒ d² - 8d = 0

⇒ d (d - 8) = 0

⇒ d = 8 cm    [∴ d ≠ 0 ]

Hence, the diameter of the of the circle is 8 cm.