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Mathematics

Consider the following two statements:

Statement 1: If the circumference of a circle is 10π cm, then its area is 25π cm2.

Statement 2: The area of a circle is π times its circumference.

Which of the following is valid?

  1. Both the statements are true.

  2. Both the statements are false.

  3. Statement 1 is true, and Statement 2 is false.

  4. Statement 1 is false, and Statement 2 is true.

Mensuration

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Answer

Given that the circumference is 10π cm.

⇒ 2πr = 10π

⇒ r = 10π2π\dfrac{10π}{2π}

⇒ r = 5 cm

Now, calculate the area using this radius,

⇒ A = πr2

= π.52

= 25π cm2.

∴ Statement 1 is true.

We know that,

Circumference of the circle = 2πr

2πr × π = 2π2r ≠ πr2.

∴ Statement 2 is false.

∴ Statement 1 is true, and Statement 2 is false.

Hence, option 3 is the correct option.

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