Question

The areas of two concentric circles are 1386 $c{m}^2$. The width of the ring is

(a) 2.8 cm (b) 3.5 cm (c) 4.2 cm (d) 3.8 cm

Answer 1

Given: The areas of two concentric circles are 1386 sq.cm and 1886.5 sq.cm. respectively.

The width of the ring = larger radius - smaller radius (of the concentric circle)
$w=R-r$

Area of larger circle = $\pi R^2$

$1886.5=\frac{22}{7}\left(R^2\right)$

$1886.5\times \frac{7}{22}=R^2$

$85.75\times 7=R^2$

$600.25=R^2$

$R=\sqrt{600.25}$

$R=24.5cm$

Area of smaller circle $=\pi r^2$

$1386=\frac{22}{7}\left(r^2\right)$

$1386\times \frac{7}{22}=r^2$

$63\times 7=r^2$

$r^2=441$

$r=\sqrt{441}$

$r=21cm$

Width of the ring(formed by concentric circles) $=R-r$

$=24.5-21=3cm$

∴Width of the ring = 3cm