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On increasing the diameter of a circle by 40%, its area will be increased by ____.

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Detailed Solution

On increasing the diameter of a circle by 40%, its area will be increased by 96%.
Suppose the original diameter is 100 units.
So, the radius is given as:

⇒ r = 1002 ⇒ r = 50

The area of the circle with radius r is given as

π r 2 .

So, the area is given as:

⇒ π × 502 ⇒ 2500 π

And, the diameter is increased by

40 % .

Thus, the new radius is given as:

⇒ r = 100 + 40 2 ⇒ r = 1402 ⇒ r = 70

So, the new area is

⇒ π × 702 ⇒ 4900 π

So, the percentage increase in the area is given as:

= 4900 π − 2500 π 4900 π × 100 = 96 %

Therefore, 96% is the correct answer.

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