Question

if the area of circle is increased by 56.25%. Find the percentage change in radius of circle?​

Answer 1

Answer:

25%

Step-by-step explanation:

Let, initially the radius be r and when it got increased, it becomes R.

% change in area is (change in area)/initial area  * 100%

⇒ % change(area) = 56.25%

⇒ [πR² - πr²]/πr² * 100%= 56.25%

⇒ π(R² - r²)/πr² = 56.25/100

⇒ (R² - r²)/r² = 0.5625

⇒ (R²/r²) - (r²/r²) = 0.5625

⇒ (R²/r²) - 1 = 0.5625

⇒ (R/r)² = 1.5625 = (1.25)²

⇒ R/r = 1.25

 Therefore,

% change in radius = (R - r)/r  * 100%

            = [ (R/r) - (r/r)  ] * 100%

            = [ 1.25 - 1 ] *100%

             = 25%