Circles
Area of Circle is [tex]\pi d^{2} /4[/tex]
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) = [tex]\pi r^{2}[/tex]
A = [tex]\pi (d/2)^{2}[/tex]
A = [tex]\pi d^{2} /4[/tex]
The area of circle is [tex]\pi d^{2} /4[/tex]
(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%
