Area of circle 1 with diameter 26cm:

\(\pi r^{2} = \pi \times (\frac{26}{2})^{2} \)

= \(169 \pi cm^{2}\)

Area of circle 2 with diameter 20 cm:

\(\pi R^{2} = \pi \times (\frac{20}{2})^{2}\)

= \(100 \pi cm^{2}\)

Area between the two circles = \((169 - 100) \pi cm^{2}\)

= \(69 \pi cm^{2}\)