If the Area of the Circle is Numerically Equal to Twice Its Circumference Then What is the Diameter of the Circle? - Mathematics

Sum

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

Solution

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"

⇒ d= 8d

⇒ d- 8d = 0

⇒ d (d - 8) = 0

⇒ d = 8 cm    [∴ d ≠ 0 ]

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

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APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 18 Area of Circle, Sector and Segment
Exercise 18A | Q 4 | Page 819