Let r be the original radius.

The area of the circle is equal to \pi r^{2}

When the radius is increased by 1 cm, the area becomes

\pi ( r+ 1)^{2}

Therefore,

\pi (r+1)^{2} - \pi r^{2} = 22

\pi(r^{2}+2r +1) - \pi r^{2} = 22

\pi r^{2} + 2 \pi r + \pi - \pi r^{2} = 22

2\pi r + \pi = 22

2 \frac{22}{7} r + \frac{22}{7} = 22

Dividing the equation by 22,

\frac{2}{7}r + \frac{1}{7} = 1

\frac{2r + 1}{7} = 1

2r + 1 = 7

2r = 6

r = 3

Therefore, the original radius of the circle was 3 cm

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