If the radius of a circle is increased by 20%. Then the area of the ci

1.	If the radius of a circle is increased by 20%. Then the area of the circle is increased by:1. 25%2. 44%3. 12%4. 36%
Answer» Correct Answer - Option 2 : 44% Given: Increased radius = 120% of Original radius Formula used: Area of circle = πr² Calculation: Let the original radius be r and the increased radius is R. Increased radius = 120% of Original radius ⇒ R = 120/100 × r ⇒ R = 6/5 × r Original raea = πr² Increased area = πR² ⇒ Increased area = π × (6/5 × r)² ⇒ Increased area = 36/25 × π × r² Required percentage = (Increased area – original area)/Original area × 100 ⇒ Required percentage = (36/25 × π × r² – πr²)/ πr² × 100 ⇒ Required percentage = (11/25 × πr²)/ πr² × 100 ⇒ Required percentage = 11 × 4 ⇒ Required percentage = 44% ∴ The area of the circle is increased by 44%.

If the radius of a circle is increased by 20%. Then the area of the circle is increased by:1. 25%2. 44%3. 12%4. 36%

Answer» Correct Answer - Option 2 : 44%

Given:

Increased radius = 120% of Original radius

Formula used:

Area of circle = πr²

Calculation:

Let the original radius be r and the increased radius is R.

Increased radius = 120% of Original radius

⇒ R = 120/100 × r

⇒ R = 6/5 × r

Original raea = πr²

Increased area = πR²

⇒ Increased area = π × (6/5 × r)²

⇒ Increased area = 36/25 × π × r²

Required percentage = (Increased area – original area)/Original area × 100

⇒ Required percentage = (36/25 × π × r² – πr²)/ πr² × 100

⇒ Required percentage = (11/25 × πr²)/ πr² × 100

⇒ Required percentage = 11 × 4

⇒ Required percentage = 44%

∴ The area of the circle is increased by 44%.

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