The radii of two circles are in the ratio 3 : 8. If the difference between their areas is 2695 π cm², find the area of the smaller circle.

Let the two radii of two circles be 3a and 8a.

The difference between their areas = 2695 π cm²

⇒ π x (8a)² - π x (3a)² = 2695 π

⇒ π x 64a² - π x 9a² = 2695 π

⇒ π x (64a² - 9a²) = 2695 π

⇒ $\cancel{π}$ x (64a² - 9a²) = 2695 $\cancel{π}$

⇒ 64a² - 9a² = 2695

⇒ 55a² = 2695

⇒ a² = $\dfrac{2695}{55}$

⇒ a² = 49

⇒ a = $\sqrt{49}$

⇒ a = 7 cm

The radii are 3a and 8a = 3 x 7 cm and 8 x 7 cm = 21 cm and 56 cm

Area of smaller circle = π x (21)²

$= \dfrac{22}{7} \times 441\\[1em] = \dfrac{9,702}{7} \\[1em] = 1,386 \text{ cm}^2$

Hence, the area of smaller circle is 1,386 cm².