Question

if the radius of a circle is increased by 50%, its area is increased by how much %

Answer 1

Given :-

If the radius of a circle is increased by 50%

To Find :-

Increase in area

Solution :-

Let the radius be R

Original radius = πR²

Now

New Radius = R + 50% of R

New Radius = R + 50/100 × R

New Radius = R + 5/10R

New Radius = 10R + 5R/10

New Radius = 15R/10

New Radius = 1.5R

Finding new are

New area = π(1.5R)²

New area = π × 2.25R²

New area = 2.25πR²

Finding % Increase in Area

Increase in % = (New Area - Original Area/Original Area × 100)

Increase in % = (2.25πR² - πR²/πR² × 100)

Increase in % = (1.25πR²/πR² × 100)

Cancel πR²

Increase in % = 1.25 × 100

Increase in % = 125 %