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Circles
Area of Circle is
Total percentage increase in the area of the modified circle is 69%
Explanation:
(a) Given the diameter of the circle be d
Then the radius of the circle = r = d/2
and the area of the circle is given by:
Area(A) =
A =
A =
The area of circle is
(b)
The increase in percentage while changing the dimensions is given by the formula :
Total % increase = a% + b% - (a% * b%)/100
Where ,
a% is the percentage increase in side a
b% is the percentage increase in side b
Let the percentage increase in radius is : a%
Since a% = b%
So the formula is
Total increase % = a% + a% + (a% * a%)/100
Given here the diameter of the circle increases by 30% so a =30
Therefore, putting the value of a in the formula
Total increase % = 30% + 30% + (30% *30%)/100
Total increase % = 60% + 9%
Total increase % =69%
Therefore the total percentage increase in the area of the modified circle is 69%