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

The areas of two concentric circles are 1386 cm² and 962.5 cm². The width of the ring is 3.5 cm.

Explanation:

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  = 962.5

`=> 22/7xx"r"^2 = 962.5`

`⇒ r^2 = (962.5 × 7/22) "cm"^2`

`=>"r"^2 = 6737.5/22`

`=> "r"^2 = 306.25`

`=> "r"^2 = sqrt(306.25)`

= 17.5 cm

∴ Width of the ring = (R – r)

`= 21 - 17.5  "cm"`

= 3.5 cm