Question

two coins of diameter 2cm and 4cm respectively are kept one over the other as shown in the figure,find the area of the shaded ring shaped region in square cm.

Answer 1

See the below picture

Answer 2

$\huge{\underline{\underline{\blue{\mathfrak{Answer :}}}}}$

★ Given :

There are two coins of diameter 2cm and 4cm.

___________________

★ Solution :

Radius of smaller coin = 1 cm

Area of smaller coin = πr²

$\sf{area = \frac{22}{7} ( {1)}^{2} } \\ \\ \sf{area = \frac{22}{7} {cm}^{2} }$

$\rule{200}{2}$

Radius of bigger coin = 2cm

$\sf{area = \pi \: {r}^{2} } \\ \\ \sf{area = \frac{22}{7}( {2)}^{2} } \\ \\ \sf{area = \frac{22}{7} \times 4 } \\ \\ \sf{area = \frac{88}{7} {cm}^{2} }$

$\rule{200}{2}$

Now,

Area of shaded region = Area of bigger coin - Area of smaller coin

$\sf{area = \frac{88}{7} - \frac{22}{7} } \\ \\ \sf{ area = \frac{88 - 22}{7} } \\ \\ \sf{area = \frac{66}{7} {cm}^{2} } \\ \\ \boxed{ \green{ \sf{area = \frac{66}{7} {cm}^{2} }}}$