In the figure below, how much more is the perimeter of the larger circle than that of the smaller circle?

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Solution

Let the radius of the smaller circle be r cm.

∴ Radius of the larger circle = (r + 1) cm

Perimeter of the smaller circle = 2πr cm

Perimeter of the larger circle = 2π(r + 1) cm = (2πr + 2π) cm

Difference between the perimeters of the larger circle and smaller circle

= {(2πr + 2π) − 2πr} cm

= 2π cm

Therefore, perimeter of the larger circle is 2π more than the perimeter of the smaller circle.

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