The shaded portion of the figure, given alongside, shows two concentric circles.

If the circumference of the two circles be 396 cm and 374 cm, find the area of the shaded portion.

Circumference of the circle = 2πr

For outer circle,

$⇒ 2 \times \dfrac{22}{7} \times R = 396\\[1em] ⇒ \dfrac{44}{7} \times R = 396\\[1em] ⇒ R = \dfrac{396 \times 7}{44}\\[1em] ⇒ R = \dfrac{9 \times 7}{1}\\[1em] ⇒ R = 63 \text{ cm}$

For inner circle,

$⇒ 2 \times \dfrac{22}{7} \times r = 374\\[1em] ⇒ \dfrac{44}{7} \times r = 374\\[1em] ⇒ r = \dfrac{374 \times 7}{44}\\[1em] ⇒ r = \dfrac{17 \times 7}{2}\\[1em] ⇒ r = 59.5 \text{ cm}$

Area of shaded portion = π(R² - r²)

= π(63² - 59.5²) cm²

= π(3,969 - 3,540.25) cm²

= π x 428.75 cm²

= $\dfrac{22}{7}$ x 428.75 cm²

= 22 x 61.25 cm²

= 1,347.5 cm²

Hence, the area of the shaded portion is 1,347.5 cm².