Question

The diameters of two concentric circles are 14cm and 12 CM. The area of the region between them is :
(A)13π cm²
(B) 52π cm²
(C) 4π cm²
(D) 8π cm²​

Answer 1

Answer: 13π cm² [option (A)]

Explanation: Diameter of smaller circle = 12 cm

Radius of smaller circle = 6 cm

Diameter of bigger circle = 14 cm

Rdius of bigger circle = 7 cm

Area of region between them = Area of bigger circle – Area of smaller circle

= πr² – πr²

= π (r² – r²)

= $\frac{22}{7}$ (49 – 36)

= $\frac{22 × 13}{7}$ = $\frac{286}{7}$ = 40.85 cm²

=> 40.85 cm² = 13π cm²

Answer 2

$r = \frac{14}{2} = 7$

$r = \frac{12}{2} = 6$

$= \pi \: {r}^{2} - \pi \: {r}^{2}$

$= \pi( {r}^{2} - {r}^{2} )$

$= \frac{22}{7} ( {7}^{2} - {6}^{2} )$

$= \frac{22}{7} (49 - 36)$

$= \frac{22}{7} \times 13$

$= \frac{286}{7}$

$= 40.857$

$= (A) \: 13π \: cm²$