Question

6. Consider a circle of diameter d cm.

Answer 1

Circles

Area of Circle is $\pi d^{2} /4$

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) = $\pi r^{2}$  

A = $\pi (d/2)^{2}$

A = $\pi d^{2} /4$

The area of circle is $\pi d^{2} /4$

(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%