Question

The radius of a circle is increased
by 50%, the perimeter of the circle
will increased
by-​

Answer 1

GIVEN :-

• Radius of circle is increased by 50%.

TO FIND :-

• Percent increase in area.

TO KNOW :-

★ Perimeter of circle = 2πr

SOLUTION :-

Let Radius of circle be 'r' initially.

Initial Perimeter = 2πr ------(1)

____________

Now , the radius is increased by 50%.

New radius = r + [50% of r]

New radius = r + [ (50/100) × r]

New radius = r + [r/2]

New radius = 3r/2

New Perimeter = 2π(3r/2)

New Perimeter = 3πr -------(2)

% increased in Perimeter ,

= [(New Perimeter - Initial Perimeter)/Initial Perimeter] × 100

= [(3πr - 2πr)/2πr] × 100

= (πr/2πr) × 100

= 50%

Hence , when radius of circle is increased by 50% , perimeter is increased by 50%.

MORE TO KNOW :-

★ Perimeter of rectangle = 2(l+b)

★ Perimeter of square = 4 × side

★ Perimeter of rhombus = 4 × side

★ Perimeter of parallelogram = 2(l+b)

★ Perimeter of semi-circle = r(2+π)