Question

if the radius of a circle is increased by 50% the perimeter of the circle will increased by

Answer 1

perimeter is also increased by 50%

Answer 2

Answer:

The perimeter of the circle will be increased by  50%

Step-by-step explanation:

Given

The percentage of increase in radius =  50%

To find,

The percentage increase in perimeter

Recall the formula

The perimeter of a circle = $2\pi r$, where r is the radius

Solution:

The percentage increase in radius = 50%

New radius = r + $\frac{50}{100}$×r = $\frac{100+50}{100}$ ×r = $\frac{3}{2}$r

Perimeter of the circle  = $2\pi r$

Perimeter of the circle when radius is $\frac{3}{2}$r = $2\pi \frac{3}{2} r$ = $3\pi r$

Increase in perimeter =  $3\pi r$ - $2\pi r$ = $\pi r$

Percentage increase in perimeter = $\frac{\pi r}{2\pi r} X100$%

= 50%

∴ Increase in perimeter =  50%

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