Q. Radius of a circle is increased by 10 %, find the percentage increase in area.
Ans. You can get the answer by using the formula below:
Percentage increase in the area = 
Percentage increase in the area =
Percentage increase in the area = 21
Percentage increase in the area =
Percentage increase in the area = 21
The answer is 21.
But how do I get the formula?
Let me explain below.
Area of a circle = A= 
Suppose the radius is increased m%
New Area = ^{2} "\pi \times \left ( r + \frac{rm}{100} \right )^{2}")
New Area =^{2} "\pi \times \left ( \frac{100r+rm}{100} \right )^{2}")
New Area = "\pi \times \left ( \frac{10000r^{2}+200r^{2}m+r^2{m^{2}}}{10000} \right )")
New Area =
Increase in the area = –
Increase in the area =
Percentage increase in the area =
Percentage increase in the area =
New Area =
New Area =
New Area =
Increase in the area = New Area – Original Area
Increase in the area =
Percentage increase in the area = Increase X 100
Orignal
Orignal
Percentage increase in the area =
Percentage increase in the area =
Good! Please post some more tricks
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