Question

The areas of two concentric circles are 1386 cm² and 962.5 cm². The width of the ring is

Options

•  2.8 cm

• 3.5 cm

• 4.2 cm

• 3.8 cm

Answer 1

3.5 cm

Let r cm and R cm be the radii of two concentric circles.

Thus, we have:

πR² = 1386

`=> 22/7xx"R"^2 = 1386`

`rArr "R" = (1386xx7/22) "cm"^2`

⇒ R² = 441 cm² 

⇒ R = 21 cm

Also,

πr2  = 962.2

`=> 22/7xx"r"^2 = 962.2`

`⇒ r2 = (962.2 × 7/22) "cm"^2`

`=> "r"^2 = (962.2/10xx7/22)"cm"^2`

`=>"r"^2 =1225/4  "cm"^2`

 `=> "r" = 35/2  "cm"`

∴ Width of the ring = (R - r)

`= (21 - 35/2) "cm"`

`= 7/2 "cm"`

= 3.5 cm