Question

On decreasing the radius of a cirde by 30%, its area is decreased by
(a) 30%
(b) 60%
(c) 45%
​

Answer 1

Answer:

• Option (D) Non of these.

Step-by-step explanation:

⇝Let initial radius be " r ".

⇝ Initial area = πr²

⇝ Final radius = r - r × 30/100

⇝ Final radius = r - 30r/100

⇝ Final radius = 100 - 30r/100

⇝ Final radius = 70r/100

⇝Final radius = 0.7r

⇝ Final area = πr²

⇝ Final area = π(0.7r)²

⇝Final area = 0.49πr²

Now, We know that,

Descresed area = Initial area - Final area / Initial area × 100.

[ Putting values ]

⇝ Descresed area = πr² - 0.49πr² / πr² × 100

⇝ Descresed area = (1 - 0.49) × 100

⇝ Descresed area = 0.51 × 100

⇝ Descresed area = 51%